- #1
jumbogala
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Homework Statement
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.
Homework Equations
The Attempt at a Solution
First I need to find fX|Y (x|y). To do this I need to take f(x,y) and divide by fY(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/ye-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?