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