Thread: Joint PDF

I am stuck on this first bit of a question:
The joint PDF of X and Y is given by
f(x, y) = cxe^{-x} x>0, |y|<x

(a) Determine the constant c.

Originally Posted by ulysses123

I am stuck on this first bit of a question:
The joint PDF of X and Y is given by
f(x, y) = cxe^{-x} x>0, |y|<x

(a) Determine the constant c.

Integrate the given joint pdf over the region defined by x > 0 and -x < y < x and equate the result to 1:

.

Solve for c.

I guess y takes values from -x to x because |y|< x ?

that cant be right if |Y|<x integrating from 0 to x leaves out half the values,
since |Y|<x
-x<y<x

Originally Posted by ulysses123

that cant be right if |Y|<x integrating from 0 to x leaves out half the values,
since |Y|<x
-x<y<x

Yes, I made a careless mistake which I have now fixed. Not that it's difficult to make the simple correction to what I originally posted.