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Math Help - Poisson distribution

  1. #1
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    Poisson distribution

    Let X be a discrete random variable with Poisson distribution with parameter \lambda

    1) Show that:

    E(X^2)=\sum_{k=1}^{\infty} \frac{ke^{-\lambda} \lambda^k}{(k-1)!}

    2) By changing the summation variable, show that E(X^2)=\lambda E(X)+\lambda

    3) Using (2), show that Var(X)=\lambda
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Let X be a discrete random variable with Poisson distribution with parameter \lambda

    1) Show that:

    E(X^2)=\sum_{k=1}^{\infty} \frac{ke^{-\lambda} \lambda^k}{(k-1)!}

    2) By changing the summation variable, show that E(X^2)=\lambda E(X)+\lambda

    3) Using (2), show that Var(X)=\lambda
    Read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Thanks so much. That answered my question completely.
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