how to derive E[Y(Y-1)]...(poisson)....

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- Aug 9th 2008, 02:58 AM #1

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- Aug 2008
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- Aug 9th 2008, 03:29 AM #2
$\displaystyle E[Y(Y-1)] = E\left[Y^2 - Y\right] = E\left[Y^2\right] - E[Y]$.

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.

- Aug 9th 2008, 03:32 AM #3
Actually you might find this thread more useful: http://www.mathhelpforum.com/math-he...tributiom.html