Question

Suppose X is a random variable with a mean of 10 and a variance of 100. Suppose Y is a random variable with a mean of 2 and a standard deviation of 16. Also, suppose X and Y are independent. What is the mean of 10 X + 3 Y?

Answer 1

`E(10x + 3y) =106`

Explanation:

Given

`E(x) =10`

`Var(x) = 100`

`E(y) =2`

`Var(y) = 16`

Required

`E(10x + 3y)`

To do this, we make use of the following equation

`E(ax + by) =aE(x) + bE(y)`

So, we have:

`E(10x + 3y) =10 * E(x) + 3 *E(y)`

`E(10x + 3y) =10 * 10 + 3 *2`

`E(10x + 3y) =100 + 6`

`E(10x + 3y) =106`