# Joint PDF

• Sep 30th 2010, 12:06 AM
ulysses123
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.
• Sep 30th 2010, 02:51 AM
mr fantastic
Quote:

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:

$\displaystyle \displaystyle 1 = c \int_{x = 0}^{x = +\infty} \int_{y = -x}^{y = x} x e^{-x} \, dy \, dx$.

Solve for c.
• Sep 30th 2010, 03:04 AM
amul28
I guess y takes values from -x to x because |y|< x ?
• Sep 30th 2010, 03:04 AM
ulysses123
that cant be right if |Y|<x integrating from 0 to x leaves out half the values,
since |Y|<x
-x<y<x
• Sep 30th 2010, 03:07 AM
mr fantastic
Quote:

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.