Suppose that X and Y are independent random variables with E

Suppose that X and Y are independent random variables with E(X) = 2, Var(X) = 5, E(Y) = -3 and Var(Y) = 6. Determine
a) E(3X-2Y) = ?
b) Var(3X-2Y) = ?

Solution

a)

E(3X-2Y)=3E(X)-2E(Y)=3*2-2*(-3)=12

b) X and Y are independent So, the covariance is zero.

Var(3X-2Y)=9Var(X)+4Var(Y)=9*5+4*6=69