# Valid joint probability density function?

• Sep 30th 2012, 11:17 AM
drabbie
Valid joint probability density function?
I have to show that this is a valid joint probability density function. My understanding is that this is valid when the integral is equal to 1. My question is, how to do I do a joint integration when only one of the variables is in play?

f(x,y) = 1/y for 0<x<y, 0<y<1

I appreciate the help!
• Sep 30th 2012, 11:27 AM
Plato
Re: Valid joint probability density function?
Quote:

Originally Posted by drabbie
I have to show that this is a valid joint probability density function. My understanding is that this is valid when the integral is equal to 1. My question is, how to do I do a joint integration when only one of the variables is in play?
f(x,y) = 1/y for 0<x<y, 0<y<1

Is the function non-negative everywhere?

What is $\displaystyle \int_0^1 {\int_0^y {\frac{1}{y}dxdy} }=~?$
• Sep 30th 2012, 12:05 PM
drabbie
Re: Valid joint probability density function?
They did not specifically say 0 elsewhere, but I assume it is non-negative outside of the limits. I will try it like that, thank you.