- #1

jumbogala

- 423

- 4

## 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 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**

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

^{-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?