I put some more thought into this and managed to figure it out on my own (it happened to be on change of variables...a topic my teacher never covered).
This problem has been irritating me for a couple days now. I can't figure it out.
The only part I really need help with is determining the joint pdf. I can figure out the rest, given what the pdf is. I would appreciate any input!!!Let denote a random sample from a distribution . Find the joint pdf of and . Note that the support of is . Also find the marginal pdf of each and . Are and independent?
I promised Chris in a pm that when I had a few moments I'd log on and reply. So here's my two cents (hopefully we both agree!):
1. I assume and are independent so that their joint pdf is given by .
2. Now note that and .
Therefore .
3. Therefore, by the change-of-variable formula, the joint pdf of and is given by
.