# Homework Help: Joint Probability Density Function

1. Feb 25, 2013

### twoski

1. The problem statement, all variables and given/known data

The joint probability density function of X and Y is given by
f(x, y) = c( x3 + xy/4 )

0 < x < 1
0 < y < 2

(a) For what value of c is this a joint density function?
(b) Using this value of c, compute the density function of Y .
(c) Using this value of c, nd PfX > Y g.

3. The attempt at a solution

I'm looking through my notes and i can't find anything that helps me solve A... :(

2. Feb 25, 2013

### LCKurtz

The double integral, over the region, of the density function must be 1.

3. Feb 26, 2013

### twoski

So the idea is, if i do a double integral on this function i should end up with c * some value, and i need to find a value for c such that c * some value = 1?

4. Feb 26, 2013

### Ray Vickson

Try it yourself to see!

5. Feb 26, 2013

### twoski

So i did it and i ended up with 3/4 * c... So the idea now is that i want C to equal 1?

And how would i start computing the density function of Y?

Last edited: Feb 26, 2013
6. Feb 26, 2013

### Ray Vickson

Do you not understand that you want the double integral = 1? That means that you need to equate your result to 1.

As to the density of Y: it will just be the *marginal* density of Y. The meaning of this was already dealt with in another thread.

7. Feb 28, 2013

### twoski

Okay i've managed to figure out everything except for the last question. I have formulas for P( X ≤ x ) but it's asking me to find P( X < Y ).

8. Feb 28, 2013

### LCKurtz

Draw a picture of that region inside your given domain and integrate the joint density over it.