Difficulty setting up double integrals for Joint Distributions

**Eugenie** · 09-30-2012 03:18 AM

Originally Posted by jimmy brooks

hedgie, i hope you don't mind but i'm itching to practice the tags...

this is my interpretation of your last line:

$\int_{0} ^{2} \int_{0}^{x_1} \frac {1}{2}*dx_2 * dx_1$

ahah. I see now how you can insert latex code in your messages. very nice.

**Eugenie** · 09-30-2012 03:24 AM

So in LaTEX, the change of coordinates formula for a density is
$g(u,v) \,du dv = f(\Phi(u,v)) |D\Phi| \, du dv = f(x,y) \, dx dy$
where
$(x,y) = (\Phi_1(u,v), \Phi_2(u,v))= \Phi(u,v)$
and
$|D\Phi| = \left|\begin{array}{ll}\frac{\delta x}{\delta u} & \frac{\delta x}{\delta v} \\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right|$

....let's see if that worked...

ahah...awesome

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