A little Poisson

[Little Fishy]

this was part of a problem on an exam i did today... I'm not sure if I did it right so I wanted to post it here and see how some proability wizzes would do it.

Let Z be a function of a random Variable Y

were Z is 2(Y^2) for any value of Y

and Y is the Poisson distribution for Lamda = 3.5

what is the expected value of Z??

thanks in advance,
little fishy

[Luzion]

I dont understand the question....

Is this a transformation variable question, or you asking that Y = the poisson distribution, and you are squaring it and then multiplying it by 2?

Im guessing that if it is the latter, wouldnt the E(X) of Z simply be (3.5^2) * 2? Since mean of Poisson equals its lamba parameter? Im confused...

[alThor]

[ QUOTE ]

were Z is 2(Y^2) for any value of Y

and Y is the Poisson distribution for Lamda = 3.5

what is the expected value of Z??


[/ QUOTE ]

The long way or the easy way? The easy way is if you are allowed to use the information that the mean and variance of Y are both lambda. Then E(Y^2) is lambda + lambda^2. Then E(Z) is 2(lambda + lambda^2).

Harder way: figure out the infinite sum of 2f(x)x^2 where f() is the Poisson pdf.

Hopefully I am not so tired that I screwed up.

alThor