Proof : Let X be a random variable and a, b be any constants.

\begin{eqnarray*}V[aX+b]&=&E[\{(aX+b)-E[aX+b]\}^{2}]\\&=&E[\{a(X-E[X])+(b-b)\}^{2}]\ \ \ (\ \text{∵}\ \ E[aX+b]=aE[X]+b\ \ )\\&=&E[a^{2}\left(X-E[X]\right)^{2}]\\&=&a^{2}E[\left(X-E[X]\right)^{2}]\ \ \ (\ \text{∵}\ \ E[a]=a\ \ )\\&=&a^{2}V[X]\end{eqnarray*}