# Joint density

• March 31st 2010, 04:50 AM
Matharch
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.
• March 31st 2010, 06:00 AM
amul28
what did u get if u do directly
with 0 to1/2 dx and 0 to 1/3 dy
• March 31st 2010, 07:20 PM
Matharch
I tried to go directly buy I still get the wrong answer.
• March 31st 2010, 08:49 PM
matheagle
try drawing the region....

$\int_0^{1/3}\int_y^{1/2}3xdxdy$
• April 1st 2010, 06:50 AM
Matharch
Quote:

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