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  1. #1
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    Question one more...

    how to derive E[Y(Y-1)]...(poisson)....
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  2. #2
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    Quote Originally Posted by students View Post
    how to derive E[Y(Y-1)]...(poisson)....
    $\displaystyle E[Y(Y-1)] = E\left[Y^2 - Y\right] = E\left[Y^2\right] - E[Y]$.

    To find $\displaystyle E\left[Y^2\right]$ read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html

    Get $\displaystyle E[Y]$ in a similar way.


    You can also get $\displaystyle E\left[Y^2\right]$ and $\displaystyle E[Y]$ from the moment generating function. For the derivation of the moment generating function read this thread: http://www.mathhelpforum.com/math-he...tribution.html. If you haven't learnt about the moment generating function then forget I mentioned it.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    $\displaystyle E[Y(Y-1)] = E\left[Y^2 - Y\right] = E\left[Y^2\right] - E[Y]$.

    To find $\displaystyle E\left[Y^2\right]$ read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html

    Get $\displaystyle E[Y]$ in a similar way.


    You can also get $\displaystyle E\left[Y^2\right]$ and $\displaystyle E[Y]$ from the moment generating function. For the derivation of the moment generating function read this thread: http://www.mathhelpforum.com/math-he...tribution.html. If you haven't learnt about the moment generating function then forget I mentioned it.
    Actually you might find this thread more useful: http://www.mathhelpforum.com/math-he...tributiom.html
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