# Math Help - Prove E[X(X-1)] = mu(mu-1)+sigma2

1. ## Prove E[X(X-1)] = mu(mu-1)+sigma2

let $E(X)=\mu$ and $Var(X)=\sigma^2$

Show that $E[X(X-1)] = \mu(\mu-1)+\sigma^2$

2. ## Re: Prove E[X(X-1)] = mu(mu-1)+sigma2

$Var(x)=E((X-\mu)^2)=E(X^2-2\mu X+\mu ^2)$

$=E(X^2)-2\mu E(X)+\mu ^2$

$=E(X^2)-2\mu ^2 + \mu ^2 = E(X^2)-\mu ^2$

So we have $E(X^2)=Var(x)+\mu ^2$

You should be able to use this last line to help you in your proof. Can you take it from here?

3. ## Re: Prove E[X(X-1)] = mu(mu-1)+sigma2

Yes, I have it now. I was making different substitutions, but somehow missed the one you gave. :/
Thanks!