Problem 2
Suppose $p(x, y, z)$, the joint probability mass function of the random variables
X, Y, and Z, is given by
$p(1, 1, 1) = \frac{1}{8}$, $p(2, 1, 1) = \frac{1}{4}$,
$p(1, 1, 2) = \frac{1}{8}$, $p(2, 1, 2) = \frac{3}{16}$,
$p(1, 2, 1) = \frac{1}{16}$, $p(2, 2, 1) = 0$,
$p(1, 2, 2) = 0$, $p(2, 2, 2) = \frac{1}{4}$
What is $E[X|Y = 2]$? What is $E[X|Y = 2, Z = 1]$?
