Math Help - If two random variable have teh joint density

1. If two random variable have teh joint density

If two random variable have the joint density given by

$f(x,y) = \begin{cases} 2e^{-2y} e^{-x} & 0 0 & otherwise \end{cases}$

Are X and Y independent ?

2. Hello,

If you can write the joint pdf as the product of a function which only depends on x, and a function which only depends on y, then they're independent.

3. You can see that they are indep by inspection and that the mariginal densities are

$f_X(x)=e^{-x}I(x>0)$

and

$f_Y(y)=2e^{-2y}I(y>0)$

an exponential and a gamma.

4. Originally Posted by Moo
Hello,

If you can write the joint pdf as the product of a function which only depends on x, and a function which only depends on y, then they're independent.
i didnt understand .......could u please elaborate