# Math Help - How do you use moment generating functions to find pdfs?

1. ## How do you use moment generating functions to find pdfs?

We never went over this in class, and it's not in the book, but there were 3 problems like it on the exam, and I got all 3 wrong, and the prof doesn't give solutions.

So, for instance, how do you use the fact that the moment generating function of the Gaussian is e^(mt+t^2sigma^2/2) to find the pdf for Z(n)=sqrt(n)*(xbar(n)-mu/sigma)?

2. Originally Posted by zhupolongjoe
We never went over this in class, and it's not in the book, but there were 3 problems like it on the exam, and I got all 3 wrong, and the prof doesn't give solutions.

So, for instance, how do you use the fact that the moment generating function of the Gaussian is e^(mt+t^2sigma^2/2) to find the pdf for Z(n)=sqrt(n)*(xbar(n)-mu/sigma)?
You can use the basic properties of MGF.

$M_{a + bX} = e^{at}M_X (bt)$

Then examine the resulting MGFs...