Question

Y = 3X - 2
Var(X) = .72
Var(Y) = 9Var(X)

where did the 9 come from?

Answer 1

Var(Y)=E((Y-E(Y))^2)=E((3X-2-(3E(X)-2))^2)=E((3X-3E(X))^2)=
=E((3^2)(X-E(X))^2)=9E((X-E(X))^2)=9Var(X).

Var(aX)=(a^2)Var(X)