(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The joint density of X and Y is given by

f(x,y) = [e^{-x/y)}e^{-y}] / y

x is between 0 and infinity; y is between 0 and infinity

Show E[X |Y = y] = y.

Jump to the last part of this post in bold if you just want to check my calculus calculations and skip the probability stuff.

2. Relevant equations

3. The attempt at a solution

First I need to find f_{X|Y}(x|y). To do this I need to take f(x,y) and divide by f_{Y}(y).

I think it's the latter which is messing me up. My understanding is that to find it, I need to integrate f(x,y) with respect to x.

The solutions manual does that, but there are no limits on their integral. Shouldn't the limits be from 0 to infinity?

They have [(1/y)e^{-x/y}e^{-y}] / [e^{-y}∫ (1/y)e^{(-x/y)}dx ] = (1/y)e^{-x/y}

Which in my calculations doesn't work out! I get -1/y. What am I doing wrong?

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# Homework Help: Applied Probability Calculation not Working Out! (Integrals)

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