- #1

Scootertaj

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**1. Let the joint pdf be f(x,y) = 2 ; 0<x<y<1 ; 0<y<1**

Find E(Y|x) and E(X|y)

Find E(Y|x) and E(X|y)

## Homework Equations

E(Y|x) = [itex]\int Y*f(y|x)dy[/itex]

f(y|x) = f(x,y) / f(x)

## The Attempt at a Solution

f(x) = [itex]\int 2dy[/itex] from 0 to y = 2y

f(y|x) = f(x,y)/f(x) = 1/2y

E(Y|x) = [itex]\int Y/2Y dy[/itex] from x to 1 = [itex]\int 1/2 dy[/itex] from x to 1

= -(x-1)/2

= (1-x)/2

The answer is supposed to be (1+x)/2