$E(X^2)$ and $VAR(X^2)$ if X is N(0,1).

Sep 2011
392
7
Mumbai (Bombay),Maharashtra,India
Hello,
I want to compute Expected value of $X^2$ and variance of $X^2$ if X be $\mathcal{N}(0,1)$ random variable. Now let $Y=X^2$ So, $f_Y(y)=\frac{2}{2\sqrt{y}}*\frac{1}{\sqrt{2\pi}}*e^{\frac{-y}{2}}$ now how to compute $E(X^2)$ and $VAR(X^2)?$

Answer to $E(X^2)=1$ How is that computed? If any member knows the correct answer, may reply.(Thinking)