so they are clearly dependent.
It certainly doesn't matter if you have normality or not.
If you differentiate wrt x and y you get
Likewise if , then
First I would like to clear up some misunderstanding I have about independence. In my text I have:
If , then X and Y are indep.
However, in my notes from class I have:
If , then X and Y are indep.
Which is correct?
Is this the only way to show independence? Does it have anything to do with expectation values? I had a question in which I had:
I was first asked to find the followings: and here is what I did:
, for this I took the 3rd derivative of the moment generating function and got this expression:
I was then asked about whether X and Y are independent. Naturally I attempted to use what I just did: therefore dependent. Is this correct?
The formula for obtaining the density of is right under
Derivation of the pdf for one degree of freedom
on Chi-square distribution - Wikipedia, the free encyclopedia
But X and Y do not have a joint distribution in .