tag:blogger.com,1999:blog-55035011589664637422024-02-18T19:51:29.321-08:00Probabilidad y estadísticaFederico Gonzalezhttp://www.blogger.com/profile/09459850363323630962noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5503501158966463742.post-24604670431495642192013-09-06T01:00:00.002-07:002013-12-18T06:51:08.158-08:00<div class="separator" style="clear: both; text-align: center;">
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Práctica 1</div>
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Problema 1</div>
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Problema 2</div>
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Problema 3</div>
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Problema 4</div>
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Ejercicio 1</div>
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Problema 1</div>
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Problema 2</div>
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Práctica 2</div>
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Problema 1</div>
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Problema 2</div>
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Problema 3</div>
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Problema 4</div>
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Ejercicio 2 "3 de octubre 2013"</div>
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Práctica 1 problema 1 en matlab</div>
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Práctica 1 problema 2 en matlab </div>
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Práctica 1 problema 3 en matlab</div>
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Práctica 1 problema 4 en matlab</div>
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Problema 2</div>
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Problema 3</div>
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Problema 4</div>
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Problema 5</div>
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Práctica 3</div>
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Problema 1</div>
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Problema 2</div>
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Problema 3</div>
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Problema 4</div>
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Ejericios PDF (Introducción a las probabilidades empleando excel)</div>
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SUÁREZ, Mario, (2012), Interaprendizaje de Probabilidades y Estadística Inferencial con Excel, Winstats y Graph, Primera Edición. Imprenta M & V, Ibarra, Ecuador.</div>
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Ejercicio 3</div>
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Ejercicio 6</div>
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Ejercicio 9</div>
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Ejercicio 12</div>
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Ejercicio 15</div>
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Ejercicio 18</div>
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Ejercicio 21</div>
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Ejercicio 24</div>
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Ejercicio 27</div>
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Ejercicio 30</div>
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Ejercicio 33</div>
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Ejercicio 36</div>
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Ejercicio 39</div>
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Práctica 4<br />
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Problema 1<br />
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Problema 2<br />
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Problema 3</div>
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Problema 4 </div>
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Problema 5<br />
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Problema 6</div>
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Problema 7<br />
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Teorema de Bayes<br />
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El teorema de Bayes se utiliza para revisar probabilidades previamente calculadas cuando se posee nueva información. Desarrollado por el reverendo Thomas Bayes en el siglo XVII, el teorema de Bayes es una extensión de la probabilidad condicional.<br />
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La interpretación más aceptada del teorema de Bayes, es que su estructura permite el calculo de probabilidades después de haber sido realizado un experimento (probabilidades aposteriori), basándose en el conocimiento de la ocurrencia de ciertos eventos que dependan del evento estudiado, o sea, se parte de probabilidades conocidas antes de efectuar el experimento (probabilidades apriori). Continuando nuestro análisis sobre el teorema de Bayes, la probabilidad condicional de Ai dado B, para cualquier i, es:<br />
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Ejemplo:<br />
Una compañía de transporte público tiene tres líneas en una ciudad, de forma que el 45% de los autobuses cubre el servicio de la línea 1, el 25% cubre la línea 2 y el 30% cubre el servicio de la línea 3. Se sabe que la probabilidad de que, diariamente, un autobús se averíe es del 2%, 3% y 1% respectivamente, para cada línea.<br />
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1) Calcular la probabilidad de que, en un día, un autobús sufra una avería<br />
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2) ¿De qué línea de transporte es más probable que un autobús sufra una avería?<br />
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A1 = Cubre el servicio de la línea 1<br />
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A2 = Cubre el servicio de la línea 2 <br />
A3 = Cubre el servicio de la línea 3 <br />
B1 = Sufre una avería <br />
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Dados:<br />
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P(A1) = 45% = 0.45<br />
P(A2) = 25% = 0.25<br />
P(A3) = 30% = 0.30<br />
P(B1|A1) = 0.02<br />
P(B1|A2) = 0.03<br />
P(B1|A3) = 0.01<br />
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1) Calcular la probabilidad de que, en un día, un autobús sufra una avería<br />
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P(B1) = (PA1)* P(B1|A1) + (PA2)* P(B1|A2) + (PA3)* P(B1|A3)<br />
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P(B1) = (0.45*0.02) + (0.25*0.03) + (0.3*0.01) = 0.0195<br />
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2) ¿De qué línea de transporte es más probable que un autobús sufra una avería?<br />
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Se debe calcular las tres probabilidades empleando el Teorema de Bayes<br />
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P(A1|B1) = (P(A1)*P(B1|A1))/P(B1) = (0.45*0.02)/0.0195 = 0.4615<br />
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P(A2|B1) = (P(A2)*P(B1|A2))/P(B1) = (0.25*0.03)/0.0195 = 0.3846<br />
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P(A3|B1) = (P(A3)*P(B1|A3))/P(B1) = (0.3*0.01)/0.0195 = 0.1538<br />
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Entonces, sabiendo que el autobús sufre una avería, lo más probable es que sea de la línea 1, ya que esta probabilidad es la mayor. <br />
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FUENTE<br />
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[1] SUÁREZ, Mario, (2012), Interaprendizaje de Probabilidades y Estadística Inferencial con Excel, Winstats y Graph, Primera Edición. Imprenta M & V, Ibarra, Ecuador.[2] sites.upiicsa "1.3.5 Teorema de Bayes" [Fecha de consulta: 2 de noviembre del 2012]. Disponible en : http://www.sites.upiicsa.ipn.mx/polilibros/portal/Polilibros/P_terminados/Probabilidad/doc/Unidad%201/1.3.5.htm#item0</div>
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Ejercicio 31 de octubre<br />
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Problema 1<br />
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Problema 2<br />
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Problema 3, 4, 5, 6</div>
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Problema 7</div>
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Problema 8<br />
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Problema 9<br />
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Problema 10<br />
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Problema 11<br />
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Problema 12<br />
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Práctica 5<br />
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Problema 1<br />
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Problema 2<br />
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Problema 3<br />
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Problema 4<br />
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Problema 5<br />
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Práctica 6</div>
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Ejercicios en Matlab 90 y 91</div>
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Ejercicios p<span style="text-align: center;">á</span>gina 92 (1,2,3)</div>
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Ejercicios en Matlab 93, 95, 97, 99</div>
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Ejercicios p<span style="text-align: center;">ágina 98 </span></div>
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Ejercicios en Matlab 101, 103</div>
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Ejercicios p<span style="text-align: center;">ágina 103 (1,2,3)</span></div>
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Práctica 6 parte 2</div>
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Problema 1</div>
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Problema 2</div>
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Problema 3</div>
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Problema 4</div>
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Problema 5</div>
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Problema 6</div>
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Problema 8</div>
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Federico Gonzalezhttp://www.blogger.com/profile/09459850363323630962noreply@blogger.com0