Thread: X and Y joint pdf probability question

If X and Y have the joint pdf

then find

Originally Posted by wik_chick88

If X and Y have the joint pdf

then find

What thoughts have you had? Where are you stuck?

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

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.

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.