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carterjavon6929
08.12.2020 •
History
Which pair of phrases best completes this table comparing the Democratic-
Republican and Federalist parties?
A. (1) Was supported by rich merchants; (2) Strictly interpreted the
Constitution
B. (1) Wanted closer ties to France; (2) Called for a larger national
army
C. (1) Was supported by poor farmers; (2) Demanded equal rights for
women
D. (1) Refused to participate in the War of 1812; (2) was supported
by rich merchants
Solved
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Ответ:
La probabilidad pedida es![0.717](/tpl/images/1328/1102/3f70f.png)
Explanation:
Primero comencemos definiendo la variable aleatoria. Para nuestro problema, la variable aleatoria es la siguiente :
La variable aleatoria
será entonces una variable aleatoria continua.
Sabemos que sigue una distribución exponencial con una media de 600 hs.
Esto se escribe :
En donde λ es igual a la inversa de la media. Esto se escribe :
λ![=\frac{1}{E(X)}](/tpl/images/1328/1102/1450f.png)
En donde
es la media de la variable. Por ende, si reemplazamos los datos del ejercicio obtenemos ⇒
λ
⇒ λ ![=\frac{1}{600}](/tpl/images/1328/1102/5a045.png)
Si reemplazamos el valor de λ en (I) obtenemos :
La función de distribución de
(por ser una variable aleatoria exponencial) es :
Si reemplazamos el valor de λ en la función de distribución de
obtenemos :
Dado que la variable aleatoria
se distribuye de manera exponencial, el hecho de saber que el sistema ha estado funcionando sin fallas durante 400 hs no nos aporta ninguna información sobre lo que ocurrirá después. Esta característica se conoce como propiedad de perdida de memoria de la variable aleatoria exponencial. Entonces, la probabilidad pedida se reduce a calcular :
Dado que saber que el sistema ha estado funcionando sin fallas durante 400 hs no nos dice nada sobre lo que ocurrirá instantes posteriores a esas 400 hs.
Calculamos entonces la probabilidad pedida :