Thread: Multivariate Distributions

1. )If the joint probability density of X and Y is given by
f(x,y)=24xy, if 0<x<1, 0<y<1, x+y<1
and 0 elsewhere


Find P(X+Y<1/2)


2.)Find the joint probability density of the two random variables X and Y whose joint distribution function is give by
F(x,y)=(1-e^(-x^2))(1-e^(-y^2)) if x>0, y>0
and 0 elsewhere

Originally Posted by Yan

1. )If the joint probability density of X and Y is given by
f(x,y)=24xy, if 0<x<1, 0<y<1, x+y<1
and 0 elsewhere


Find P(X+Y<1/2)

.

Originally Posted by Yan

2.)Find the joint probability density of the two random variables X and Y whose joint distribution function is give by
F(x,y)=(1-e^(-x^2))(1-e^(-y^2)) if x>0, y>0
and 0 elsewhere

As is separable you can assume that is separable (can be written as the product of two one variable functions each in one of the two variables)

So:



and:





.