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

Let X and Y have JD f(x,y) = e^-y, 0<x<y

Find:

a) E(X|Y=y), E(Y|X=x)

b) density function of R.V. E(X|Y), E(Y|X)

3. The attempt at a solution

a)

I have found E(X|Y=y) = y/2 for y>= 0

E(Y|X=x) = x +1 for x>= 0

by finding fx(x) = ∫(x to infinity) e^-y dy = e^-x

f(y|x) = (e^-y)/ (e^-x)

so E(Y|X=x) = ∫( x to inifinty) y* (e^-y)/ (e^-x) dy = x +1

I was wondering if u actually take the integral from x to INFINITY since the RESTRICTION is 0<x<y.

b) E(X|Y=y) = Y/2 for y>= 0

E(Y|X=x) = X +1 for x>= 0

I was wondering for this question if you just convert the x and y to capital letters? or if i am suppose to do something else

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# Homework Help: Density function of random variables E(X|Y) and E(Y|X)

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