Calculating Conditional Distribution: Difficulty Setting up Double Integral

Hi,

The problem is as follows:

The joint probability density function of X and Y is given by
f(x,y) = 1/8(y^2-x^2)e^-y, -y<=x<=y, 0<y<infinity

A) Find the conditional distribution of X, given Y = y. I know that I must set up a double integral, but I don't quite understand how to set up the limits of integration. Could someone explain that?

Also, X and Y are dependent, since X's parameters depends on Y, correct?

Thanks!

Hey SC313.

Is there any relationship between Y and X such that f(X,Y) = blah (an example Y = X + 3)? If this is the case then these will be used to setup your limits of integration.

I think the limits are implying the relationship for you since -y <= x <= y and in this case you have your answer.

As a note we usually either supply the limits, or we supply the connection between the random variables for the constraint such that f(X,Y) = c where c is a constant and f(X,Y) = a function of X and Y (like Y-X or XY).