# Thread: 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

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

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

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

and

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

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

5. Originally Posted by wolfyparadise
i didnt understand .......could u please elaborate
You have been told how to do this. You are expected to have sufficient understanding of things so that explanations such as those given make sense.

Go back to your textbook or class notes and review this material. Also, click on 5.2 here: Probability density function - Wikipedia, the free encyclopedia

6. Originally Posted by wolfyparadise
i didnt understand .......could u please elaborate
no mite