Thread: Dice problem (obtaining expected value)

1. Dice 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!

X has binomial distribution: $\displaystyle P(X=i)=\binom{60}{i}\left(\frac{1}{6}\right)^i$$\displaystyle \left(\frac{5}{6}\right)^{60-i}. So, \displaystyle E(X^2)=\sum_{i=1}^{60}i^2P(X=i). 3. Re: Dice problem (obtaining expected value) Originally Posted by emakarov X has binomial distribution: \displaystyle P(X=i)=\binom{60}{i}\left(\frac{1}{6}\right)^i$$\displaystyle \left(\frac{5}{6}\right)^{60-i}$. So, $\displaystyle E(X^2)=\sum_{i=1}^{60}i^2P(X=i)$.
$\displaystyle Var(X)=E(X^2)-\overline{X}^2$

CB