[SOLVED] bivariate RVs, joint and marginal densities, and transformations
Hello, I'd like some help on this tough problem. Thanks in advance!
Given the joint density:
find the joint density function
and find out if U, V are independent.
My work for this part of the problem:
I got a joint density function
is that correct? and also, how do I integrate that with the crazy exponents? or is there a simpler way to test for independence other that checking
The second part of the problem:
Let the transformation from (X,Y) -> (R,θ) be defined as
find the joint density and marginal densities.
So far on this part I have it solved for X and Y:
I tried plugging in the equations into each other but I don't know how to get rid of the tan(). Any help is appreciated.