Suppose X and Y are independent random variables X has mean

Suppose X and Y are independent random variables, X has mean 65 and standard deviation 11, Y has mean 15 and standard deviation 3, calculate the mean and standard deviation of the following:

2Y+20

Solution

Given, E(Y)=15 and Std Dev(Y)=3, i.e., Var(Y)=9

Therefore, mean of 2Y+20,

E(2Y+20) = 2E(Y)+20 = 2 x 15 + 20 = 50

Standard deviation of (2Y+20) is Var(2Y+20)^1/2

Var(2Y+20) = 4 Var(Y) = 4 x 9 = 36

Therefore, std dev (2Y+20) = 6