# Thread: factorial moment generating function

1. ## factorial moment generating function

2. $E(t^X)=\sum_{x=0}^n{n\choose x}t^xp^x(1-p)^{n-x}$

$=\sum_{x=0}^n{n\choose x}(tp)^x(1-p)^{n-x}$

Use the binomial theorem

$(pt+(1-p))^n$

If you differentiate and let t=1, you will obtain E(X)=np.

Differentiate a second time and let t=1 and you will find $E(X(X-1))$

This should work well with the Poisson too.

3. Thank you for the response. I have been trying to figure out what you mean about the differentiation. I don't know what to differentiate. Could you ne a little more specific? Thank you

4. differeniate wrt t, then let t=1
it says that in the problem

I'm really busy grading exams this weekend
plus I have a galley proof to review