tag:blogger.com,1999:blog-23686831977438842532024-02-22T01:15:21.496-08:00Diario de BioestadisticaSarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-2368683197743884253.post-43229573287345231232014-11-20T14:51:00.000-08:002014-11-20T14:51:40.316-08:00DISTRIBUCIÓN DE PROBABILIDADES EN CIENCIAS DE LA SALUD<!--[if gte mso 9]><xml>
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<br />
<div class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="color: #e46c0a; font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #E46C0A; mso-style-textfill-fill-colortransforms: lumm=75000; mso-style-textfill-fill-themecolor: accent6; mso-themecolor: accent6; mso-themeshade: 191;">DISTRIBUCIÓN DE
PROBABILIDAD EN SALUD</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span style="color: #e46c0a; font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #E46C0A; mso-style-textfill-fill-colortransforms: lumm=75000; mso-style-textfill-fill-themecolor: accent6; mso-themecolor: accent6; mso-themeshade: 191;">¿Para Qué? ¿Por qué?
</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%;">Es importante el uso de la
probabilidad en el campo de la salud para los niveles de organización de las
distintas enfermedades que padezca una población, para conocer el error que
pueda existir en un diagnostico, y las medidas que puedan tomarse ante ello, de
manera que al tener presente una enfermedad existan los valores positivo
negativo, Si ó No, y así tener <span style="mso-spacerun: yes;"> </span>una
estabilidad en el momento de organizar las enfermedades que se presenten en una
determinada población. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-weight: bold;">Cuando
un profesional en el área de la salud utiliza métodos para
evaluar los alcances que puede tener por ejemplo una enfermedad o un
medicamento, en las distintas poblaciones, se puede llegar a tener
mas certeza de cual es el diagnostico adecuado que se le va a
realizar a los distintos pacientes, se define como una función que asigna
a cada suceso definido sobre la variable aleatoria, la probabilidad de que
dicho suceso ocurra.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
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<span style="color: #e46c0a; font-family: "Arial","sans-serif"; font-size: 18.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #E46C0A; mso-style-textfill-fill-colortransforms: lumm=75000; mso-style-textfill-fill-themecolor: accent6; mso-themecolor: accent6; mso-themeshade: 191;">Ejemplo:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">Una profesional en el campo de la salud de 32 años de
edad necesita saber si se encuentra embarazada, ya que tiene ausencia de la
menstruación, se le realiza un examen de orina, donde los valores pueden ser
positivo o negativo. Dando como resultado positivo, la señora ya puede estar
segura que tendrá un bebe, mientras que la Doctora tratante obtuvo un
diagnostico exitoso. Según la distribución de Bernoulli que tomo una
probabilidad de éxito y fracaso. En este caso positivo representa el éxito. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMPEd3C79v1gWyk4rgkwcT0Nwo1DVamS18IfaHTYZvKsoyS1m5PZfiE4A3pm8wFaZ5b3vPJtXOz5rNkfqev98wSsKF-7XNgOCf5yMFGWHlnr9v1awQCwzOHlPBxiR00Shclrt3hiaWz9hj/s1600/embarazada.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMPEd3C79v1gWyk4rgkwcT0Nwo1DVamS18IfaHTYZvKsoyS1m5PZfiE4A3pm8wFaZ5b3vPJtXOz5rNkfqev98wSsKF-7XNgOCf5yMFGWHlnr9v1awQCwzOHlPBxiR00Shclrt3hiaWz9hj/s1600/embarazada.gif" height="400" width="366" /></a></div>
<br />
<span style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-ansi-language: ES; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;">Con respecto a la
distribución de probabilidad la inferencia estadística consiste en extraer una
manera de una población y analizar sus datos con el propósito de aprender
acerca de ello. Muchas veces se tiene un conocimiento superficial de la función
de masa de probabilidad o de la función de densidad de probabilidad de la
población. En estos casos la función de masa o de densidad </span>Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-12939165176207322012014-11-15T09:12:00.002-08:002014-11-15T09:12:45.630-08:00Esperanza, Varianza y Desviación Estándar<b><span style="background-color: #b45f06;"><br /></span>
</b><br />
<div style="text-align: justify;">
<b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUu71Ctch-RPZtcafU8mcpn5XEU2quMDQCRBiX9fOsrRStwQF_Vas9uwbbw2pjyHxkYpK4oRgYyGuQOIFARHGGdYdPszFQUVa-hrevvusvNGwJQAa1zLjc96vw64Mg-Zk_Wd-6cfjE0HPk/s1600/varianza.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUu71Ctch-RPZtcafU8mcpn5XEU2quMDQCRBiX9fOsrRStwQF_Vas9uwbbw2pjyHxkYpK4oRgYyGuQOIFARHGGdYdPszFQUVa-hrevvusvNGwJQAa1zLjc96vw64Mg-Zk_Wd-6cfjE0HPk/s1600/varianza.jpg" height="240" width="320" /></a><span style="font-size: large;"><span style="color: orange;">Varianza</span></span></b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
La
Varianza de unos datos es la media aritmetica del cuadrado de las
desviaciones respecto a la media de la misma. Se simboliza como <i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2 y se calcula aplicando la fórmula: </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<span style="color: orange;"><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=∑<i>i</i>=1<i>N</i>(<i>xi</i>−<i>x</i>¯)2<i>N</i>=(<i>x</i>1−<i>x</i>¯)2+(<i>x</i>2−<i>x</i>¯)2+…+(<i>xN</i>−<i>x</i>¯)2<i>N</i></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">que se puede simplificar como: </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<span style="color: orange;"><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=∑<i>i</i>=1<i>Nx</i>2<i>iN</i>−<i>x</i>¯2=<i>x</i>21+<i>x</i>22+…+<i>x</i>2<i>NN</i>−<i>x</i>¯2</span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"> </a><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Del mismo modo que para la media,
no siempre será posible encontrar la varianza, y es un parámetro muy sensible a
las puntuaciones extremas. Se puede observar que al estar la desviación elevada
al cuadrado, la varianza no puede tener las mismas unidades que los datos.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Comparando con el mismo tipo de
datos, un varianza elevada significa que los datos están más dispersos.
Mientras que un valor de la varianza bajo indica que los valores están por lo
general más próximos a la media.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Un valor de la varianza igual a
cero implica que todos los valores son iguales, y por lo tanto también
coinciden con la media aritmética.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="color: orange;"><b><u><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Propiedades de la
varianza:</span></u></b></span><br />
<span style="color: orange;"><br /></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; mso-pagination: none; tab-stops: 36.0pt; text-autospace: none; text-indent: -18.0pt;">
<span lang="ES-EC" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: ES-EC; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2≥ La varianza es un valor positivo, como ya se ha comentado
anteriormente, la igualdad sólo se da en el caso de que todas las muestras sean
iguales.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; mso-pagination: none; tab-stops: 36.0pt; text-autospace: none; text-indent: -18.0pt;">
<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Si a todos los datos
se les suma una constante, la varianza sigue siendo la misma.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; mso-pagination: none; tab-stops: 36.0pt; text-autospace: none; text-indent: -18.0pt;">
<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Si todos los datos se
multiplican por una constante, la varianza queda multiplicada por el cuadrado
de la constante.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; mso-pagination: none; tab-stops: 36.0pt; text-autospace: none; text-indent: -18.0pt;">
<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Si se disponen de
varias distribuciones con la misma media y se calculan las distintas varianzas,
se puede hallar la varianza total aplicando la fórmula </span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">21+</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">22+…+</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2<i>nn</i></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">En el caso de que las
distribuciones tengan distinto tamaño, la fórmula se pondera y queda como</span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">21<i>k</i>1+</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">22<i>k</i>2+…+</span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2<i>nknk</i>1+<i>k</i>2+…+<i>kn</i></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="color: orange;"><br /></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="color: orange;"><b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Ejemplo 1</span></b></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">La altura en cm de los estudiantes
de la Facultad de Medicina está en la siguiente tabla. Calcular la varianza.</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: .5pt; mso-padding-alt: 0cm .5pt 0cm .5pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: .05pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">xi</span></i></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">fi</span></i></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 1;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[160,170)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">165</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">1</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 2;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[170,180)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">175</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 3;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[180,190)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">185</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">4</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 4;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[190,200)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">195</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">3</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 141.25pt;" width="188"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[200,210)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 58.7pt;" width="78"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">205</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 25.05pt;" width="33"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: .5pt; mso-padding-alt: 0cm .5pt 0cm .5pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: .05pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">xi</span></i></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">fi</span></i></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">xifi</span></i></div>
</td>
<td style="background: white; border-left: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">x</span></i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2<i>ifi</i></span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 1;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[160,170)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">165</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">1</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">165</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">27225</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 2;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[170,180)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">175</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">350</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">61250</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 3;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[180,190)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">185</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">4</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">740</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">136900</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 4;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[190,200)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">195</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">3</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">585</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">114075</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 5;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">[200,210)</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">205</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">410</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">84050</span></div>
</td>
</tr>
<tr style="height: .05pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td style="background: white; border-top: none; border: solid black 1.0pt; height: .05pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 123.85pt;" width="165"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 51.55pt;" width="69"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 36.65pt;" width="49"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">12</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 66.4pt;" width="89"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2250</span></div>
</td>
<td style="background: white; border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: .05pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0cm .5pt 0cm .5pt; width: 96.55pt;" width="129"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">423500</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Se debe calcular la media </span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">x</span></i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">¯=225012=187.5</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">para poder aplicar la fórmula.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Se calcula entonces la varianza </span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">ω</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=42350012−187.52=135.42</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="color: orange;"><b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Ejemplo 2</span></b></span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">En un examen de Anatomía de los
estudiantes de Odontología, todos los alumnos de la clase sacaron un diez.
Hallar la varianza de las notas.</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Al coincidir todos los valores la
media coincide también con ellos <i>x</i>¯=10, y la varianza es nula </span><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">σ</span></i><span lang="ES-EC" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: ES-EC;">2=0.</span></div>
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<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">LA DESVIACIÓN
ESTÁNDAR </span></b></span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Es <i>una medida de la cantidad típica en la que los valores del
conjunto de datos difieren de la media.</i> Es la medida de dispersión más
utilizada, se le llama también desviación típica. La desviación estándar
siempre se calcula con respecto a la media y es un mínimo cuando se estima con
respecto a este valor.</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Se calcula de forma sencilla, si se conoce la varianza, por cuanto que
es la raíz cuadrada positiva de esta. A la desviación se le representa por la
letra minúscula griega "sigma" (δ</span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">) </span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">ó
por la letra S mayúscula, según otros analistas</span></div>
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<span style="color: orange;"><i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Cálculo de la Desviación Estándar</span></i></span></div>
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<b><span style="color: orange;"><i><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">δ = √δ2 </span></i><i><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">ó
S = √S2</span></i></span></b></div>
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<b><span style="color: orange;"><u><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Propiedades de la Desviación Estándar:</span></u></span></b></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">A su vez la desviación estándar, también tiene una serie de propiedades
que se deducen fácilmente de las de la varianza (ya que la desviación típica es
la raíz cuadrada positiva de la varianza):</span></div>
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<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">La desviación
estándar es siempre un valor no negativo S será siempre ³ 0 por definición.
Cuando S = 0 è X = xi (para todo i).</span></div>
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<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Es la medida de
dispersión óptima por ser la más pequeña.</span></div>
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<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">La desviación
estándar toma en cuenta las desviaciones de todos los valores de la variable</span></div>
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<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Si a todos los
valores de la variable se le suma una misma constante la desviación estándar no
varía.</span></div>
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<span lang="es" style="font-family: Symbol; font-size: 14.0pt; mso-ansi-language: #000A; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span>Si a todos los
valores de la variable se multiplican por una misma constante, la desviación
estándar queda multiplicada por el valor absoluto de dicha constante.<b style="mso-bidi-font-weight: normal;"><i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;"> </span></i></b></div>
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<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><i><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Ejemplo:</span></i></b></span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">1.- Del calculo de la varianza de las edades de cinco estudiantes
universitarios de segundo semestre de Nutrición <span style="mso-spacerun: yes;"> </span>se obtuvo </span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">δ2=2</span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">3.45</span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;"> como la desviaci</span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">ón
estándar es la raíz cuadrada positiva, entonces </span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">δ = √2</span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">3.45</span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">= </span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">4,8</span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;"> años.</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2.- Igual procedimiento<span style="mso-spacerun: yes;"> </span>se aplica
para encontrar le desviación estándar de las cuentas por pagar del Laboratorio Biomerca,
recordemos que la varianza obtenida fue de 566.000, luego entonces la desviación
estándar es igual a </span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;">δ =√</span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">566000</span><span lang="EL" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: EL;"> = </span><span style="font-family: "Arial","sans-serif"; font-size: 14.0pt;">752,3
bolívares. </span></div>
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<span style="color: orange;"><b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">ESPERANZA MATEMÀTICA </span></b></span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">En estadistica
la <b>esperanza matemática</b> (también llamada <b>esperanza</b>,valor<b> esperado</b>,
<b>media poblacional</b> o <b>media</b>) de una variable aleatoria</span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">, es el número </span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">que formaliza la idea
de <i>valor medio</i> de un fenómeno aleatorio.</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Cuando
la variable aleatoria es discreta, la esperanza es igual a la
suma de la probabilidad de cada posible suceso aleatorio multiplicado
por el valor de dicho suceso. Por lo tanto, representa la cantidad
media que se "espera" como resultado de un experimento aleatorio
cuando la probabilidad de cada suceso se mantiene constante y el
experimento se
repite un elevado número de veces. Cabe decir que el valor que toma la
esperanza matemática en algunos casos puede no ser "esperado" en el
sentido más general de la palabra - el valor de la esperanza puede ser
improbable o incluso imposible.</span></div>
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<span style="color: orange;"><b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Propiedades: </span></b></span></div>
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<b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Constantes</span></b></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">La esperanza matemática de una constante es igual a esa misma constante,
es decir, si <i>c</i> es una constante, entonces E[<i>c</i>] = <i>c</i>.</span></div>
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<b><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Linealidad</span></b></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">La esperanza es un operador lineal ya que:</span></div>
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<img alt="" 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<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">Por ende:</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A;">Ejemplos:</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">1.- Luis Sánchez <span style="mso-spacerun: yes;"> </span>tira un dado el
valor esperado equilibrado de 6 caras es 3,5. Podemos hacer el cálculo</span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">y cabe destacar que 3,5 no es un valor posible al rodar el dado. En este
caso, en el que todos los sucesos son de igual probabilidad, la esperanza es
igual a la media aritmetica.</span><br />
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" 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<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">2.- Una aplicación común de la esperanza matemática es en las apuestas o
los juegos de azar. Por ejemplo, la ruleta americana tiene 38 casillas equiprobables. La ganancia para acertar una apuesta
a un solo número paga de 35 a 1 (es decir, cobramos 35 veces lo que hemos
apostado y recuperamos la apuesta, así que recibimos 36 veces lo que hemos
apostado). Por tanto, considerando los 38 posibles resultados, la esperanza
matemática del beneficio para apostar a un solo número es: </span><span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;"><img alt="" src="data:image/png;base64,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/> </span></div>
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<span lang="es" style="font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-ansi-language: #000A;">que es -0,0526 aproximadamente. Por lo tanto uno esperaría, en media,
perder unos 5 céntimos por cada euro que apuesta, y el valor esperado para
apostar 1 euro son 0.9474 euros. En el mundo de las apuestas, un juego donde el
beneficio esperado es cero (no ganamos ni perdemos) se llama un "juego justo".</span></div>
<br />
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Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-20831871651319110102014-11-15T08:08:00.001-08:002014-11-15T08:46:49.526-08:00Distribución de Probabilidad en el Campo de la Salud<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7jakycn_0e46UQgra6hiq37tAQoQtouIsc1rGEW5-5vdx0acLJe1hra2j_wFSO_dPrs726VNH58f4C9vb0aOz5SiovOx6GvDvDfG-D2YcXxk-ugLy4Fl1m1N8a716OrmxnBqA1VlNqCfI/s1600/Salud+y+Bienestar+SS.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7jakycn_0e46UQgra6hiq37tAQoQtouIsc1rGEW5-5vdx0acLJe1hra2j_wFSO_dPrs726VNH58f4C9vb0aOz5SiovOx6GvDvDfG-D2YcXxk-ugLy4Fl1m1N8a716OrmxnBqA1VlNqCfI/s1600/Salud+y+Bienestar+SS.jpg" height="180" width="320" /></a></div>
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<a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"> </a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"> </a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=2368683197743884253" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="color: orange;"><b><i><span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">DISTRIBUCIÓN DE PROBABILIDAD</span></i></b></span></div>
<div align="center" class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: center; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Cabe destacar la suma importancia de la Estadística en la cotidianidad,
tomando en cuenta que desde el momento que el hombre vive en sociedad necesita
de estadística, ya que en los censos, recopilaciones de datos,<span style="mso-spacerun: yes;"> </span>tarde variaciones de esos números. Los hebreos,
los egipcios, sirios, persas, griegos y romanos utilizaron la estadística para
distintos fines.</span><br />
<div style="text-align: justify;">
<br /></div>
</div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Uno de los objetivos de la estadística es el conocimiento cuantitativo
de una determinada parcela de la realidad. Para ello, es necesario construir un
modelo de esta realidad particular objeto de estudio, partiendo de la premisa
de que lo real es siempre más complejo y multiforme que cualquier modelo que se
pueda construir. De todas formas, la formulación de modelos aceptados por las
instituciones responsables y por los usuarios, permite obviar la existencia del
error o distancia entre la realidad y el modelo. Los modelos teóricos a los que
se hace referencia se reducen en muchos casos a (o incluyen en su formulación)
funciones de probabilidad. </span></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<br />
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">En el caso continuo, es decir, cuando la variable puede tomar cualquier
valor de un intervalo, la distribución de probabilidad permite determinar las
probabilidades correspondientes a con subintervalos de valores. Una forma usual
de describir la distribución de probabilidad de una variable aleatoria es
mediante la denominada función de densidad, en tanto que lo que se conoce como
función de distribución representa las probabilidades acumuladas. Una de las
preocupaciones de los científicos ha sido construir modelos de distribuciones
de probabilidad que pudieran representar el comportamiento teórico de
diferentes fenómenos aleatorios que aparecían en el mundo real. </span><br />
</div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Con respecto a la distribución de probabilidad la inferencia estadística
consiste en extraer una manera de una población y analizar sus datos con el propósito
de aprender acerca de ello. Muchas veces se tiene un conocimiento superficial
de la función de masa de probabilidad o de la función de densidad de
probabilidad de la población. En estos casos la función de masa o de densidad
de probabilidades se aproxima mediante una de muchas familias comunes de curvas
o funciones.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 5.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<br />
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>La distribución de probabilidad es para
indicar toda la variedad de valores médicos que pueden representarse como
resultado de un experimento si éste se llevase a cabo. Es decir, describe la probabilidad de que un evento se realice en el
futuro, constituye una herramienta fundamental para la prospectiva, puesto que
se puede diseñar un escenario de acontecimientos futuros considerando las
tendencias actuales de diversos fenómenos naturales.</span></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<br />
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Es importante en la medicina porque me permite conocer la frecuencia de
las enfermedades, y los valores que me arroja luego de aplicar un experimento.</span></div>
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<br /></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span style="color: #e69138;"><span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Ejemplo:</span></span></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Una joven universitaria de 25 años de edad necesita saber si se
encuentra embarazada, ya que tiene ausencia de la menstruación, se le realiza
un examen de orina, donde los valores pueden ser positivo o negativo. Dando
como resultado positivo, la joven ya puede estar segura que tendrá un bebe,
mientras que la Doctora tratante obtuvo un diagnostico exitoso. Según la distribución
de Bernoulli que tomo una probabilidad de éxito y una de fracaso<br />
</span></div>
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<div class="MsoNormal" style="mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none; text-justify: inter-ideograph;">
<span lang="es" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: #000A; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"></span></div>
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Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-71899522476086595142014-10-12T09:05:00.000-07:002014-10-12T09:34:30.809-07:00<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 14.0pt; line-height: 115%;"> </span><span style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 115%;"> </span><span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;"> </span><span style="line-height: 115%;">Problema de Salud y su
Probabilidad</span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;"> </span><span style="line-height: 115%;"> Escasez de insumos, el gran
problema de los pacientes con cáncer<o:p></o:p></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;">en Venezuela, el cáncer es
la principal causa de muerte por enfermedad según el último informe oficial de
las autoridades del país. En la actualidad, la escasez de reactivos y medicinas
derivado de las dificultades que enfrenta el mercado </span><span style="line-height: 18.399999618530273px;">cambiaros</span><span style="line-height: 115%;">.<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> Tipo: Noticia Fecha: 04/08/2014. </span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> </span></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif; margin-left: 1em; margin-right: 1em;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNv_Vzooa5V_sCIEU_-y0r_YnG8AzhWtzpzyx_ehf3NCngjQOWdpRCmTASn3lIbBPGf4Z6MzIYZcEqnQ3HVNSN5W6wcggmOpJOCz46gl41p9MweThord4bhcAeVAdESrsZYmK1N5zswuu0/s1600/Salud-hospital-medicina.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNv_Vzooa5V_sCIEU_-y0r_YnG8AzhWtzpzyx_ehf3NCngjQOWdpRCmTASn3lIbBPGf4Z6MzIYZcEqnQ3HVNSN5W6wcggmOpJOCz46gl41p9MweThord4bhcAeVAdESrsZYmK1N5zswuu0/s1600/Salud-hospital-medicina.jpg" height="213" width="320" /></a></span></div>
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<div class="MsoNormal" style="text-align: justify;">
<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> Problema: Un Estadístico estudio la
falta de insumos para pacientes oncológicos en los Hospitales. Dr. Miguel Oraá de Guanare-Portuguesa, Hospital General
Dr. Luis Razetti de Barinas y el
Instituto Autónomo Hospital Universitario de Los Andes en el mes de agosto del 2014.Con la
finalidad de determinar si genero o no problemas al buen funcionamiento de
dichos Hospitales.<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<span style="line-height: 18.399999618530273px;"><span style="font-family: Arial, Helvetica, sans-serif;"> </span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;"><span style="line-height: 18.399999618530273px;"> a)</span></span><span style="text-indent: -18pt;"> </span><span style="line-height: 115%; text-indent: -18pt;">Definir el espacio muestral de este estudio.</span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18.399999618530273px;"> b)</span><span style="line-height: 115%;"> Señalar
los elementos del evento M que consiste
en que al menos 2 de los 3 Hospitales
les afecto la falta de insumos.<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;"> c)<span style="line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%;">Enunciar los elementos del evento N que
consiste en que máximo 1 de los Hospitales
no les afecto. <o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;"> a) HDMO </span><span style="line-height: 115%;"> HGDLR IAHULA</span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;">SI o NO genero problemas SI SI SI<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> SI SI NO<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> SI NO SI<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> SI NO NO<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> NO NO NO<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> NO NO SI<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> NO SI NO<o:p></o:p></span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"> NO SI SI
<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 93.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 93.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;">b)<span style="line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%;">Evento M.( SI SI SI) ; (SI SI NO) ; (SI NO
SI) ; (NO SI SI)<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 93.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;">c)<span style="line-height: normal;"> </span></span><!--[endif]--><span style="line-height: 115%;">Evento N.( SI SI NO); ( SI NO SI); ( NO SI
SI</span><span style="line-height: 115%;"> )<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 93.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
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Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-41627427136658040752014-10-05T08:38:00.000-07:002014-10-05T08:38:15.397-07:00<div class="MsoNormal" style="text-align: justify;">
<span style="color: orange; font-family: Arial, sans-serif;"><span style="font-size: 21px;"><b><i> </i></b></span></span><b><span style="font-family: 'Times New Roman', serif; font-size: 16pt;">
</span></b><b><i><span style="color: orange; font-family: "Arial","sans-serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES;">Relación Entre Probabilidad y Salud</span></i></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"> </span><span style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 115%;">La probabilidad en relación con la salud,
mide el número que va a reflejar la frecuencia con la que ocurre un resultado.
Se puede decir que la importancia de la probabilidad en relación con la salud
radica en que gracias a ella podemos tener seguridad y certeza de experimentos
realizados y los factores de riesgo. <o:p></o:p></span></div>
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<span style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 115%;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 115%;"> Por otra parte es importante en el
campo profesional ya que sirve para el control de enfermedades y su prevención.</span><span style="font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 115%;"><span id="goog_1180007522"></span><span id="goog_1180007523"></span></span></div>
Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-667182613212646452013-12-11T12:58:00.000-08:002013-12-11T13:06:32.776-08:00Bioestadistica<br />
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<![endif]--><b style="mso-bidi-font-weight: normal;"><span style="color: #e36c0a; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: accent6; mso-themeshade: 191;"> Una Mirada a la Bioestadística</span></b><br />
<br />
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Capitulo 8: una mejor bioestadística para una
mejor ciencia médica.</span></b></div>
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<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"><span style="mso-spacerun: yes;">
</span>En la medicina y en otras ciencias de la salud, se busca cierto grado de
certeza por el cual se puede hacer una predicción de que puede suceder con un
tratamiento o cuando no va a funcionar, es importante buscar una persona que
sepa muy bien bioestadística “Si la Estadística es de buena calidad la ciencia es de buena calidad".</span></b></div>
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<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"> </span></b><img class="rg_i" data-src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcRaes1uXP6XjI5c_ykI5pnjAXB9AT1r8jDXK8j5TQ-NPwYKj15U" data-sz="f" height="132" name="Lfgze4CnAsCd5M:" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcRaes1uXP6XjI5c_ykI5pnjAXB9AT1r8jDXK8j5TQ-NPwYKj15U" style="height: 132px; margin-left: 0px; margin-right: 0px; margin-top: 0px; width: 200px;" width="200" /><span style="mso-fareast-language: ES; mso-no-proof: yes;"><span style="mso-spacerun: yes;"></span></span>
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<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Capitulo 12: el análisis demográfico y otros
procesos sociales.</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"> </span></b><b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"> </span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Dentro de la demografía hay métodos que tienen
que ver con los desarrollos matemáticos y luego se recurre a la estadística. </span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">La estadística es importante para responder a
preguntas de procesos sociales, en los cuales se encuentran dos conceptos básicos
de probabilidad:</span></b></div>
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<li><b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">En los estudios de fenómenos demográficos se
busca acercar de la mejor manera a lo que está sucediendo, para entender que
nuestro todo son probabilidades y ocurrencias y que existe un margen de error.</span></b></li>
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<br /></div>
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<li><b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">El riesgo no solo consiste en medir la
seguridad sino en explicar lo estudiado.</span></b></li>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Para los demógrafos es importante el análisis
de encuestas y acompañarse de un estadístico en cuestiones de muestreo y población.
</span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Cada vez hay más combinaciones entre los métodos
estadísticos con los demográficos y ha generado posibilidad de la observación de
cosas que no se podían hacer.</span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"><br /></span></b></div>
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<span style="mso-fareast-language: ES; mso-no-proof: yes;"><span style="mso-spacerun: yes;"> </span></span><span style="mso-fareast-language: ES; mso-no-proof: yes;"><span style="mso-spacerun: yes;"><img class="rg_i" data-src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRj0uOjqKnNp2snDZQ6AhjFVRPSuBePBSzj31e7jKVdGNK_8mrH" data-sz="f" height="200" name="wp62QfdWhroEMM:" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRj0uOjqKnNp2snDZQ6AhjFVRPSuBePBSzj31e7jKVdGNK_8mrH" style="height: 173px; margin-left: -9px; margin-right: -8px; margin-top: 0px; width: 139px;" width="160" />
</span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;"></span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">Capitulo 14: la medicina basada en evidencia estadística.</span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">El matemático y medico Alvan R. Feinstein pensó
que muchos de los aspectos médicos no eran reproducibles e hizo <span style="mso-spacerun: yes;"> </span>un libro llamado Clinimetria medición de los
aspectos clínicos, entonces él empezó a trabajar en que tanto se reproducían los
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">En la actualidad el médico se ve obligado a
entender mas los fenómenos de probabilidad, para hacer un mejor diagnostico por
lo tanto ahora se obtiene más formación en la estadística que anteriormente. </span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-themecolor: text1;">La estadística siempre va a ser necesaria en
cualquier área si desea analizar la probabilidad de la naturaleza, la
naturaleza es probabilística si no entendemos esto vamos a cometer errores.</span></b></div>
<br />
<b style="mso-bidi-font-weight: normal;"><span style="color: black; font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: ES; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-themecolor: text1;">Los métodos estadísticos
son una herramienta útil para diferenciar que es bueno o malo de los
tratamientos no es forma absoluta pero nos brinda una aproximación útil.</span></b><br />
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<br />Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0tag:blogger.com,1999:blog-2368683197743884253.post-22249156299804718392013-10-28T13:55:00.001-07:002013-10-28T13:59:49.029-07:00Bioestadística <br />
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<span style="color: orange;"><b>Introducción a la Estadística</b></span> <br />
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La Estadística esta ligada con los métodos científicos en la toma, organización recopilación presentación y análisis de datos, tanto para la deducción de conclusiones como para tomar decisiones razonables.</div>
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<b>¿Que es Bioestadística?</b> La bioestadística es una rama de la estadística que se ocupa de los problemas planteados dentro de las ciencias de la vida, como la biología, la medicina, entre otros.</div>
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<span class="Apple-tab-span" style="white-space: pre;"> </span><b>Población :</b> es el conjunto de elementos, individuos o entes sujetos a estudio de los cuales queremos obtener un resultado.</div>
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<b>Muestra :</b> es un subconjunto al que tenemos acceso y sobre el que realmente hacemos las observaciones.</div>
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<span style="color: orange;"><b> Reseña Histórica y Conceptos Básicos de Estadística</b></span><br />
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El primer medico en utilizar métodos matemáticos fue el francés Pierre Charles-Alexandre Louis ( 1787-1872 ) , en un estudio de la tuberculosis, que influyo en toda una generación de estudiantes.<br />
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<b>Población Finita :</b> tiene un numero finito o fijo. </div>
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<b>Ejemplo : </b>numero de alumnos en un centro de enseñanzas. </div>
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<b>Población Infinita : </b>tiene elementos incontables. </div>
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<b>Ejemplo :</b> conjunto de números pares.</div>
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<b style="text-align: justify;"> </b><span style="color: orange; text-align: justify;"><b>Escalas de Medición y Variable </b> </span><span style="text-align: justify;"> </span><br />
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<b>Escala Ordinal :</b> es categórica puede clasificarse de acuerdo con algún criterio de orden. </div>
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<b>Ejemplos : </b></div>
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Etapa de desarrollo de un ser vivo. </div>
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Niveles de una enfermedad<span style="text-align: left;"> </span></div>
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<b style="text-align: left;">Variable :</b><span style="text-align: left;">al observar una característica se encuentra que toma valores diferentes en personas, lugares o cosas.</span></div>
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<b>Ejemplos :</b></div>
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El peso de una persona. </div>
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Temperatura de una ciudad.</div>
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<span style="color: orange;"><b>Planificación y Ejecución de Investigaciones Medicas</b></span> <span style="text-align: justify;"> </span></div>
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<b style="text-align: justify;">Determinación de Objetivos :</b><span style="text-align: justify;"> determinar el objetivo final, es decir, explicar para que se realiza.</span></div>
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<b style="text-align: justify;">Formulación de una Hipótesis :</b><span style="text-align: justify;"> es una aplicación provisional de los hechos que no es mas que anticiparse aquellos fenómenos que pueden ocurrir, con el fin de contrastar si es cierta.</span></div>
Sarahttp://www.blogger.com/profile/09096809939877387457noreply@blogger.com0