Question

If X is normally distributed with mean 15 and variance 16, find mean & standard deviation of Y = 3X + 3

Answer 1

$E(Y)=E(3X+3)=3E(X)+3=3*45+3=138.$

$Var(Y)=Var(3X+3)=3^2Var(X)=9*16=144.$

$\sigma(Y)=\sqrt{Var(Y)}=\sqrt{144}=12.$