Re: Random Variables and inequalities

From: Robert Dodier (robert_dodier_at_yahoo.com)
Date: 10/30/04 

Date: 30 Oct 2004 08:11:01 -0700

crroush@gmail.com (decious) wrote:

> consider the Probability Denisty function: f_(n,m) (x,y) = 6/7(x^2 +
> xy/2), 0<x<1, and 0<y<2, find Pr(n>m)
>
> I am not sure how to set up this up for the case of 2 random
> variables, would you need to evaluate some inequalities or???

This problem doesn't seem to be well-posed. (1) n and m don't
appear in the right hand side of the eqn. (2) Perhaps the problem
is to find Pr(x>y) ?

I'll suppose for the moment you meant Pr(x > y). For any set A,
Pr(A) is just the integral of f over A. So Pr(x > y) is the integral
of f over the intersection of x > y (a half-plane) with the
rectangle (0 < x < 1) cross (0 < y < 2). Have at it!

Robert Dodier