Let X1,X2,X3 be three independent random variables with

Chapter 5, Problem 11E

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QUESTION:

Let \(X_1, X_2, X_3\) be three independent random variables with binomial distributions b(4, 1/2), b(6, 1/3), and b(12, 1/6), respectively. Find

(a) \(P(X_1 = 2, X_2 = 2, X_3 = 5)\).

(b) \(E(X_1X_2X_3)\).

(c) The mean and the variance of \(Y = X_1 + X_2 + X_3\).

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QUESTION:

Let \(X_1, X_2, X_3\) be three independent random variables with binomial distributions b(4, 1/2), b(6, 1/3), and b(12, 1/6), respectively. Find

(a) \(P(X_1 = 2, X_2 = 2, X_3 = 5)\).

(b) \(E(X_1X_2X_3)\).

(c) The mean and the variance of \(Y = X_1 + X_2 + X_3\).

ANSWER:

Step 1 of 5

Given,

Binomial distributions b(4, 1/2), b(6, 1/3), and b(12, 1/6).

 

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