Mean of a squared random variable if I have a random variable $x$ ~ $N(0,1)$, what is the expected value of $x^2$? Is there a general rule to calculate expected values of squared variables? Thanks.
Hint: There is a connection between the variance of $x$ and the expected value of $x^{2}$. If you write both down separately you'll see it.
If $X$ follows Standard Normal.then  $X^2$ follows Chi Square with 1 degrees of freedom..
And the Expected value of a  Chi Square is the degrees of freedom itself So $$E(X^2)=1$$
As far as a general rule, there is none you have to figure it out for yourself by practicing