Problem 33E

Let Y be a discrete random variable with mean μ and variance σ 2. If a and b are constants, use Theorems 3.3 through 3.6 to prove that

a E ( aY + b) = aE(Y ) + b = aμ + b.

b V ( aY + b) = a2 V (Y ) = a2σ 2.

Reference

Solution:

Step 1 of 3:

Here we need to prove that

a).

b).