# Math Help - one more...

1. ## one more...

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

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

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

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

You can also get $E\left[Y^2\right]$ and $E[Y]$ 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.

3. Originally Posted by mr fantastic
$E[Y(Y-1)] = E\left[Y^2 - Y\right] = E\left[Y^2\right] - E[Y]$.

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

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

You can also get $E\left[Y^2\right]$ and $E[Y]$ 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