Recall that
Var(aX + b) = a2Var(X)
and
Var(X1 + X2) = Var(X1) + Var(X1)
if the random variables X1 and X2 are independent. Use these results to show that
Var(a1X1 + ... + anXn + b)
= a12Var(X1) + ... + an2Var(Xn)
if the random variables Xi are independent.