Grinstead-Snell-Probability · Problem 6.3.9

Sums of Random Variables

Mathematics · expected-value-variance-continuous

Problem

Let

X

Y

, and

Z

be independent random variables, each with mean

\mu

and variance

\sigma^2

. (a) Find the expected value and variance of

S = X + Y + Z

. (b) Find the expected value and variance of

A = (1/3)(X + Y + Z)

. (c) Find the expected value of

S^2

and

A^2