Suppose X and Y are independent with E X 1 E Y2 varX3 and va

Suppose X and Y are independent with E X =1, E Y=2, var(X)=3, and var(Y)=1. Find the mean and variance of 3 X + 4 Y - 5

(Show work) Hint: answer= mean=6 variance=43

Mean = E( 3 X + 4 Y - 5) = 3* E(X) + 4 * E(Y) - 5 * E(0) = 3*1 + 4*2 - 5 * 1 = 3 + 8 - 5 = 6

Variance = V( 3 X + 4 Y - 5) = 3^2 * V(X) + 4^2 * V(Y) - 5(0) = 9*(3) + 16(1) = 27 + 16 + 0= 43