Basic Probability Question

[bighomage]

This class isn't too hard, but I'm not sure how to do this question and I don't have a book. I'm sure one of you knows how to do it:

X ~ Poisson(lambda = 0.8). Find E(X!).

I know that E(X) = lambda, but I'm not sure what to do with the factorial. Thanks in advance.

[kbinder]

Are you sure the exclamation point means factorial? I'm almost positive that factorials are only defined for nonnegative integers. Maybe you're being asked to calculate E(!X), where !X means not X.

[pzhon]

It's a good idea to get the text and read it, to attend class, and to ask the instructor when you don't understand. As an exercise, calculate the tuition per lecture hour.

The expected value of a discrete random variable X is

Sum x P(X=x).
x

The expected value of f(X) is

Sum y P(f(X)=y).
y

By considering the x so that f(x)=y, that is the same as

Sum f(X) P(X=x).
x

You should be able to find a closed form expression for this sum for this problem. The numerical value is in white: <font color="white">2.2466448205861079572</font>