Let X1, X2, X3 be three independent random variables with binomial distributions b(4

Chapter 5, Problem 5.3-11

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QUESTION:

Let X1, X2, X3 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(X1 = 2, X2 = 2, X3 = 5). (b) E(X1X2X3). (c) The mean and the variance of Y = X1 + X2 + X3.

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QUESTION:

Let X1, X2, X3 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(X1 = 2, X2 = 2, X3 = 5). (b) E(X1X2X3). (c) The mean and the variance of Y = X1 + X2 + X3.

ANSWER:

Step 1 of 4

Given that,

Let X1, X2, X3 be three independent random variables with binomial distributions b(4, 1/2), b(6, 1/3), and b(12, 1/6), respectively.

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