# Thread: X and Y joint pdf probability question

1. ## X and Y joint pdf probability question

If X and Y have the joint pdf
$\displaystyle f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1,$
then find $\displaystyle P (0 < X < 0.5 | y = 0.75)$

2. Originally Posted by wik_chick88
If X and Y have the joint pdf
$\displaystyle f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1,$
then find $\displaystyle P (0 < X < 0.5 | y = 0.75)$
What thoughts have you had? Where are you stuck?

3. i havent ever done a joint pdf question where the probability has the "given y = ..." in it!

4. Originally Posted by wik_chick88
i havent ever done a joint pdf question where the probability has the "given y = ..." in it!
In the first instance, I suggest you refer to your class notes or textbook for the definition of the conditional density of X given Y = y ....

After doing so, please ask for more help if required.

5. find the conditional density of X given Y
First you must find the marginal of Y and divide the joint density by that marginal
When you finally have the conditional density, plug in your value for y and integrate x over the region.
HOWEVER, since the joint density is uniform over the triangle it will be uniform over the line y=.75
since you want 0<x<.5 the answer should be 2/3 which is two-thirds of that line.
DRAW the region and you will see how obvious this is.