# Assume $E[X^2]=20$. Find the mean and variance of $X$ if the mean and variance are equal.

I've never seen a problem like this before. We're given that $E[X^2]=20$ and that the mean and variance of $X$ are equal. The task is to find the mean and variance given this information.

I wish I could say I tried everything, but I'm honestly clueless as to where I should even begin. I tried setting $Y = X^2$ to rewrite the random variable, but I don't think that helps at all.

$$Var(X)=E(X^2)-E(X)^2$$
• Did you know that $Var(X)\ge0$? – user296113 May 13 '16 at 9:08