A random variable Y is called gamma( , n) for >0 and natural n if it takes positive values and takes the following PDF:

f(y)= ( ) exp

Show how to find the moment generating function, expectation and variance of Y.

my attempt:

=

let u=

Then du= dy

=

=

Is this right so far? Is there some reason why should be one? Could somebody show me how to integrate this by parts? (I know I should be able to do it but I am really struggling).