# Thread: Marginal pdf of 2 dimensional random variables

1. ## 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)?

2. ## Re: Marginal pdf of 2 dimensional random variables

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

3. ## Re: Marginal pdf of 2 dimensional random variables

Thank you very much!

This helped a lot.