Setting the limits on an integral for a joint pdf

**veol** · April 6th 2009, 11:32 PM

Hi everyone!

I'm trying to solve a double integral to find the joint pdf of a function, but I'm not sure as to how to set the limits.

$f(x, y) = c(x^2 - y^2)e^{-x}<br />$

with $0 \leq x, -x \leq y \leq x$

I have to solve for the constant, c, so I thought that solving the double integral in the range of x and y and making that equal to 1 would solve for c, but I'm having trouble integrating. I suspect its my bounds for the integral.

I'm not quite sure.... for my integration of the x values, I set the limits from 0 to infinity, and for the y values, the limits i set were from -x to x. Is that right?

Many thanks!

**matheagle** · April 6th 2009, 11:56 PM

It seems to be $1=\int_0^{\infty}\int_{-x}^x f(x,y)dydx$ .

**veol** · April 6th 2009, 11:58 PM

Yeah, that's what I thought it would be as well. I just remember setting the limits to double integrals as being tricky for some odd reason... I felt unsure of myself.

Thanks for the heads up, matheagle!

**matheagle** · April 7th 2009, 12:11 AM

You should always draw the region. You draw the lines y=x and y=-x.
It is the region between those two in the first and fourth quadrants since x is nonnegative.

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