# Math Help - Joint density

1. ## Joint density

I have a joint density function

$f(x,y)= 3x, 0 \leq Y \leq X \leq 1$

And I have to find

$P(X \leq 1/2 , Y \leq 1/3)$

I integrated 0 to X dy and 0 to 1/3 dx

Obviously I'm doing something wrong since that is not the answer in the book. So a little help would be appreciated.

2. what did u get if u do directly
with 0 to1/2 dx and 0 to 1/3 dy

3. I tried to go directly buy I still get the wrong answer.

4. try drawing the region....

$\int_0^{1/3}\int_y^{1/2}3xdxdy$

5. Originally Posted by matheagle
try drawing the region....

$\int_0^{1/3}\int_y^{1/2}3xdxdy$

That gives me the right answer. I drew the region and that's where I made a mistake. Now it's all clear.

Thanks