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Math Help - Dice problem (obtaining expected value)

  1. #1
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    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!
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  2. #2
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    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).
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  3. #3
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    Re: Dice problem (obtaining expected value)

    Quote Originally Posted by emakarov View Post
    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
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