Joint Distributions

bobcat89

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Oct 5, 2014
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X and Y are jointly distributed non negative random variables such that their joint density is given by: f(x,y)= e-x-y for x>0 and y>0.

Find P(X+0.8>Y|X>0.6)

I get that this is a conditional probability question with joint distributions for continuous random variables therefore I am supposed to integrate but i do not know the limits to use and how the function splits. Please explain how i could do this and any further questions of this kind.
 
This will be, of course, a double integral with respect to x and y. You are told that x> 0.6 so the "outer" integral, with respect to x, is from 0.6 to infinity. You are told that, for each x, y< x+ 0.8 so the "inner" integral, with respect to y, is from 0 to \(\displaystyle x+ 0.8\).
 
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