Joint pdf question

1. Dec 16, 2004

semidevil

so X and Y have joing pdf f X Y(x, y) = 1/2 for 0 < y < x < 2, and 0 otherwise.

find P(0< Y < 2/5 | X = 3/4)

first, I dont understand how to read the function. So the function is equal to 1/2 when 0 < y < x < 2. And it is equal 0 otherwise.

So I need to find Probabilty Y is between 0 and 2/5, given that X = 3/4? is that what it is asking?

I think this has to do with integration, but what am I integrating? It's a single integeral right? and what do I do w/ the X = 3/4 part?

actually, I got it...so no need for that.

but this one. so f X Y (x,y) = c(y + x)y for 0<x<1 and 0<y<1.

I need to find c.

So I found the marginals, and what do I do to find c? am I suppose to put it against something?

Last edited: Dec 16, 2004
2. Dec 17, 2004

Popey

The total probability may be equal 1, right?

3. Dec 17, 2004

Bartholomew

You don't need to find the marginals. The integral of the function from -infinity to infinity for both x and y (which is the same as the integral from 0 to 1 for both x and y in this case) equals 1, and you just solve for c.