If X is the number of 3's that appear when 60 dice are tossed, what is the E(X^2)?

I am not sure how to set this problem up? I am guessing you have to get it into an integral form but I am not sure. Thanks to anyone who can help!

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- Oct 21st 2011, 05:13 AMacasas4Dice problem (obtaining expected value)
If X is the number of 3's that appear when 60 dice are tossed, what is the E(X^2)?

I am not sure how to set this problem up? I am guessing you have to get it into an integral form but I am not sure. Thanks to anyone who can help! - Oct 21st 2011, 06:33 AMemakarovRe: Dice problem (obtaining expected value)
X has binomial distribution: $\displaystyle P(X=i)=\binom{60}{i}\left(\frac{1}{6}\right)^i$$\displaystyle \left(\frac{5}{6}\right)^{60-i}$. So, $\displaystyle E(X^2)=\sum_{i=1}^{60}i^2P(X=i)$.

- Oct 21st 2011, 10:12 AMCaptainBlackRe: Dice problem (obtaining expected value)