If X and Y are independent normal random variables with EX

If X and Y are independent, normal random variables with E(X) = 0, V(X) = 4, E(Y) = 10, and V(Y) = 9. Determine the following:

Round your answers to four decimal places (e.g. 98.7654).

E(2X + 3Y)

Solution

By linearity,

E(2x + 3y) = 2E(x) + 3E(y)

Thus,

E(2x + 3y) = 2(0)+3(10)

= 30 [ANSWER]