Let . Set so that the two vector components will be independent.
I can get (and similarly ) as , but I can't integrate it. I suspect this isn't the right way to proceed.
The solution given is: "There is no such ."
Hello,
There is a unique C such that f_{X,Y} is a pdf (it will be the inverse of the integral of the function). We don't care about the value, we can just keep it as C. With C being different from 0, would it be possible to write the joint pdf as a product in the form g(x)*h(y) ? (which would mean that X and Y are independent)
The answer is obviously no...
Hence the answer "there is no such C"