I am revising for an exam and this question has appeared and I don't know how to tackle it. In previous parts we are asked to work out the mgf and mle of a gamma which I have done and they are (1-Bt)^-v and βhat=(1/n*v)∑xi
Now we are asked to do this:
Suppose it is known that v=5 and our sample mean has been calculated to equal 10. The resulting Gamma(v,Bhat) distribution is now our working model of the process generating the data. Write down the mgf of this distribution. Hence, or otherwise find the constant c such that, according to our working model,
Pr(X_n+1≤c) = 0.95,
where X_n+1 represents an independent draw from X that was not included in our earlier sample.
If anyone could help me on this it would be greatly appreciated, pretty sure I've included any relevant info!
Strangers keep coming over to pick up, help!