Suppose that a random variable Y has a gamma distribution w. parameters and an unknown . We have earlier proved that has a chi-square distribution w. 4 df. Using as a pivotal quantity. derive a 90% confidence interval for \beta.
I don't know if I'm on the right way. I create a new random variable and look for
I then have a similar example in the book that tells me to set it up like this:
Must I derive the pdf of U manually or can I use that is chi-square distributed and put in the pdf of a chi-square distribution?
That would be:
but with y=u and = 4
I've tried to do that but I don't get the right answer, which is .
Thanks for your help.