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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.

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6
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Hint

Use the fact that

$$Var(X)=E(X^2)-E(X)^2$$

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  • $\begingroup$ Thank you! Such a simple solution. However, I do get 2 distinct solutions in -5 and 4. $\endgroup$ – stassp May 13 '16 at 9:07
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    $\begingroup$ Did you know that $Var(X)\ge0$? $\endgroup$ – user296113 May 13 '16 at 9:08
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    $\begingroup$ Right, because it's the sum of the squared differences. My bad. $\endgroup$ – stassp May 13 '16 at 9:12

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