# A few questions.

• Oct 28th 2009, 10:01 PM
CUEngineering
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.
• Oct 28th 2009, 10:24 PM
matheagle
You need to review calculus three change of variables.
Especially the part where these use Jacobians.
You need to make a transformation from $R^2$ to $R^2$
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.
• Oct 30th 2009, 07:13 AM
CUEngineering
Could you expand on that a little bit? I'm still not quiet sure what to do
• Oct 30th 2009, 07:50 AM
matheagle
Quote:

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