Suppose X and Y have joint density f(x,y)=1 for 0

Question

Suppose X and Y have joint density f(x,y)=1 for 0<x,y<1. Find P(XY<=z)

anonymous · Answer

I'll try to get you an answer early tomorrow some time if someone hasn't answered it first. I have to look up technique and I don't want to go grab my book out from my car. It's a cool question though, I just didn't have to do it in Cal III other than knowing it was an application of multiple integrals, but I'll get with you in the morning some time with whatever I got.  Looking at it though I thought that P has to be less than 1, and is f(x,y)= 1 the function that we are considering or something else. Either way I'll have more insight tomorrow.

anonymous · Answer

It looks like it's just the double integral of x*y.  with both bounds from 0 to 1. = 1/4. Now if there is another definition for values of x and y, then you put those values in the integral. The lower bounds of dy and dx have to be at least 0, and we are only considering z as far as 1 it looks like, so there goes the upper bounds for dy dx. Let me know if you hae something more to it, but that seems to be all we are looking at.