Marginal PDF Bounds: Calculating Integration Limits

[fishies]

Hey guys,

So I'm having trouble telling what the integration bounds should be when calculation the marginal PDF of two random variables.

So the joint PDF fX1,X2(x1,x2) is a constant C = 1 in the regions x1 and x2.
The regions are bound by 0<=x1<=1 and 0<=x2<=2(1-x1).

If the marginal PDFs are defined as:
fx1 = int(-inf,inf) fX1,X2(x1,x2)*dx2
fx2 = int(-inf,inf) fX1,X2(x1,x2)*dx1

what will the integration bounds be?

Thanks for your help,
Fishies

 

[Stephen Tashi]

what will the integration bounds be?

Fishies

They will be the same as the bounds that you stated for x1 and x2. Is that what you're asking? The use of minus infinity to plus infinity in theorems involving the distribution of random variables is correct if we use the convention that the distributions are defined to be zero at places where they are otherwise "undefined". To actually perform the integrations on distributions given by algebraic expressions but restricted to finite areas, you must use bounds that restrict the integration to those areas.