If E(X), E(Y)=11, find the value of E(5X+7Y) a. 112 b. 165 c. 134 d. 142
Question
If E(X), E(Y)=11, find the value of E(5X+7Y)
a. 112
b. 165
c. 134
d. 142
Solution
Para resolver el problema, utilizamos la propiedad de la esperanza matemática (E) que dice que E(aX + bY) = aE(X) + bE(Y), donde a y b son constantes.
Dado que E(X) = 11 y E(Y) = 11, y queremos encontrar E(5X + 7Y), aplicamos la propiedad mencionada:
E(5X + 7Y) = 5E(X) + 7E(Y)
Sustituimos los valores de E(X) y E(Y):
E(5X + 7Y) = 5(11) + 7(11)
Calculamos los productos:
E(5X + 7Y) = 55 + 77
Sumamos los resultados:
E(5X + 7Y) = 132
Por lo tanto, la respuesta correcta es:
c. 134
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