I just have a few general questions.

1). Lets say I have a joint pdf f(r,h) where r is radius and h is height and the function is in terms of both r and h. How do I transform this into a joint pdf of volume and surface area?

2). I have two independent standard exponential random variables X1 and X2. I want to find the pdf of Y = X1 / (X1 + X2). How do I do this? Y is not a linear combination of X1 and X2.

3). I want to find the linear combination of a standard uniform and a standard exponential random variable. Do I just add them together?

4)> I want to find Z = XY where X and Y are both independent uniform random variables. Do I just multiply them?

I missed the lecture in class and by just looking at the notes, I have no idea how do tackle these problems so any help is appreciated. Thanks.