Question

E(X)=3, V(X)=2, E(Y)=5, and V(Y)=1. If Z=3X-5Y, calculate its expected value and variance. Please give in depth work for part b.

a) E(Z)=-16

b)V(Z)=

Answer 1

There are few formulas we need to use here:

Where, is covariance between X and Y. When X and Y are independent events then covariance is 0.

See the formula for variance, irrespective of + or - in the middle we get all terms positive in right side.

Part a) E(Z) = 3E(X) - 5E(Y) = 3*3 - 5*5 = 9 - 25 = -16

Part b)

Here taken covariance as 0 because X and Y are independent events. (If not then we will get answer in covariance form).

Hence, V(Z) = 43.

Please comment if any doubt. Thank you.