Consider two discrete random variables X and Y , with sample spaces {1,2,3} and {1,2} respec- tively, and the following joint distribution p(x, y).

p(x, y)	x=1	x=2	x=3
y=1	1/16	4/16	1/16
y=2	2/16	3/16	5/16

1. Compute the marginal distributions p(x) and p(y)
2. Compute the conditional distributions p(x | Y = 1) and p(y | X = 2)
3. Are X and Y statistically independent?
4. Compute the expectation values E[X] and E[Y ].

p(x)	p(x=1)	p(x=2)	p(x=3)
	3/16	7/16	6/16

p(y)	p(y=1)	p(y=2)
	6/16	10/16

p(x | Y=1)	p(x=1 | Y=1)	p(x=2 | Y=1)	p(x=3 | Y=1)
	1/6	4/6	1/6

p(y | X = 2)	p(y=1 | X = 2)	p(y=2 | X = 2)
	4/7	3/7

3. No