# Quick question on marginal distributions

#### mrzpn1

##### New Member
Hi, I'm trying to figure out a marginal distribution for a joint probability function. My question is - what do I use as my limits of integration?

It's given that 0<y<1-x^2 and -1 <x< 1. For integrating out y it is easy. I'm wondering about x. Do I use -1 and 1 as my limits, or + and 1 sqrt(1-y)?

Thank you!

#### fed1

##### TS Contributor
Use
Pr(X = x, Y = y)

over -1 < x < 1

Trickiness:

Notice that the Pr( Y > 1 - X^2) = 0;

This means that you do not have to integrate over that region.

#### mrzpn1

##### New Member
Ok I understand...I think.

If I'm trying to find the marginal density for f sub y...then I would have to integrate out x. I would use -1 and 1 as my limits then, and integrate the joint density function over that with respect to x?

Thanks so much for your help, btw