Let , where each .
Then by indep .
Then let and do a calc one change of variables.
OR if you wish to use MGFs...
.
Now, I don't know how you're writing your exponential/gamma densities.
BUT subtitute t/n for t in a MGF and it's over.
Let be the mean of a random sample from the exponential distribution, Exp( ). Using the mgf technique determine the distribution of .
I'm sure this is wrong, but I don't know why.
The book has the answer in the back, saying it should be , but I don't know how to get there. MGF problems often seem to give me difficulty.