Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other
Compute P(X1< X2< X3|X3<1 )
P(X1< X2< X3|X3<1 )
The Attempt at a Solution
P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1 )/ P(X3<1)
=triple integral of f(x1, x2, x3) dx1dx2dx3 as x1 goes from 0 to 1,x2 goes from x1 to x3, and x3 goes from x2 to 1.