How to Find c for Given Joint PDF?

[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 don't 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?

 

[Popey]

The total probability may be equal 1, right?

 

[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.