If X and Y have the joint pdf

$\displaystyle f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1, $

then find $\displaystyle P (0 < X < 0.5 | y = 0.75)$

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- Dec 15th 2010, 05:09 AMwik_chick88X 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 $\displaystyle P (0 < X < 0.5 | y = 0.75)$ - Dec 15th 2010, 12:14 PMmr fantastic
- Dec 15th 2010, 07:14 PMwik_chick88
i havent ever done a joint pdf question where the probability has the "given y = ..." in it!

- Dec 15th 2010, 08:39 PMmr fantastic
- Dec 16th 2010, 09:34 PMmatheagle
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.