Question

X and Y are independent variables with means 10 and 20, and variances 2 and 3 respectively. Find the variance of 3X + 4Y ?

Answer 1

Given: E(X) = 10 , E(Y) = 20, V(X) = 2 and V(Y) = 3

V(3X+4Y) = $3^2.$ V(X) + $4^2.$ V(Y) = $9\times2+16\times3=18+48=66$