# Dice problem (obtaining expected value)

• Oct 21st 2011, 06:13 AM
acasas4
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!
• Oct 21st 2011, 07:33 AM
emakarov
Re: Dice problem (obtaining expected value)
X has binomial distribution: $P(X=i)=\binom{60}{i}\left(\frac{1}{6}\right)^i$ $\left(\frac{5}{6}\right)^{60-i}$. So, $E(X^2)=\sum_{i=1}^{60}i^2P(X=i)$.
• Oct 21st 2011, 11:12 AM
CaptainBlack
Re: Dice problem (obtaining expected value)
Quote:

Originally Posted by emakarov
X has binomial distribution: $P(X=i)=\binom{60}{i}\left(\frac{1}{6}\right)^i$ $\left(\frac{5}{6}\right)^{60-i}$. So, $E(X^2)=\sum_{i=1}^{60}i^2P(X=i)$.

$Var(X)=E(X^2)-\overline{X}^2$

CB