Thread: Expected values & Moment-generating function (MGF)

Having a little trouble with this problem. Thank you in advance!

A random variable Y has a density function f(y) = e^y, y < 0.
1. Find E(e^(3Y/2))
2. Find MFG for Y.
3. Find V(Y).

Pls don't double post.

Recall

Originally Posted by charmagne

Having a little trouble with this problem. Thank you in advance!

A random variable Y has a density function f(y) = e^y, y < 0.
1. Find E(e^(3Y/2))
2. Find MFG for Y.
3. Find V(Y).

so for 1.:



which is elementary.

Now look up the definition of the MGF to do 2., and for 3. you should know that:



and both of the terms on the right can be obtained from the MGF.

CB