Hey all! I'm new here and I've scanned some posts but couldn't find anything that could help me out with this problem. Here's what I'm stuck with:
Let X and Y be two random variables with a joint probability density function f given by:
f(x, y) =
1, if −y < x < y,
0, if 0 < y < 1.
Find the marginal probability density functions of X and Y.
I've been going at this for a while now and any help would be appreciated. Thanks in advance!
You do not need to know double integrals to find a marginal PDF from a joint PDF. To find the marginal PDF of X, integrate the joint PDF with respect to Y, and set your bounds of integration as the range of Y. Similarly, to find the marginal PDF of Y, integrate the joint PDF with respect to X, and set your bounds of integration as the range of X.
Basically:
and
If you are getting stuck on solving the integral, you're going to have to post the joint PDF or at least some of your work.