# Marginal pdf of 2 dimensional random variables

• Nov 17th 2011, 12:15 PM
Marmy
Marginal pdf of 2 dimensional random variables
Hi everybody,

Given is the following joint distribution of the 2-dimensional random variable (X1,X2).

f(x1,x2)=(1/(2*x1); if 0<x2<x1 ;0<x1<2;
0; otherwise

How do I get the two marginal pdf f(x1) and f(x2)?

• Nov 18th 2011, 12:33 AM
CaptainBlack
Re: Marginal pdf of 2 dimensional random variables
Quote:

Originally Posted by Marmy
Hi everybody,

Given is the following joint distribution of the 2-dimensional random variable (X1,X2).

f(x1,x2)=(1/(2*x1); if 0<x2<x1 ;0<x1<2;
0; otherwise

How do I get the two marginal pdf f(x1) and f(x2)?

It helps if you sketch the region over which the density is non-zero:

$f_{X_1}(x_1)=\int_R f(x_1, x_2) \; dx_2=\int_{x_2=0}^{x_1} f(x_1, x_2) \; dx_2$

$f_{X_2}(x_2)=\int_R f(x_1, x_2) \; dx_1=\int_{x_1=x_2}^{2} f(x_1, x_2) \; dx_1$

CB
• Nov 20th 2011, 09:47 AM
Marmy
Re: Marginal pdf of 2 dimensional random variables
Thank you very much!

This helped a lot.