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.


1 Answer 1



Use the fact that


  • $\begingroup$ Thank you! Such a simple solution. However, I do get 2 distinct solutions in -5 and 4. $\endgroup$
    – stassp
    May 13, 2016 at 9:07
  • 2
    $\begingroup$ Did you know that $Var(X)\ge0$? $\endgroup$
    – user296113
    May 13, 2016 at 9:08
  • 1
    $\begingroup$ Right, because it's the sum of the squared differences. My bad. $\endgroup$
    – stassp
    May 13, 2016 at 9:12

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