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.
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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.
Last edited by mr fantastic; Sep 30th 2010 at 03:06 AM. Reason: Fixed careless mistake.
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.
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