A few questions.

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.

You need to review calculus three change of variables.
Especially the part where these use Jacobians.
You need to make a transformation from to
I did the product of uniforms here this past summer.
If you want Y=X1/(X1+X2) then let W=X1 and find the joint density of Y and W.
Then integrate out the random variable W.

Could you expand on that a little bit? I'm still not quiet sure what to do

Quote:

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Originally Posted by CUEngineering

Could you expand on that a little bit? I'm still not quiet sure what to do

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go to your calculus book
review the change of variable for polar in thre dimension
See how you need both mapping from rectangular to polar and back
then see how you take all the partial derivatives and then transform
to the new system