Let X and Y have following joint distribution:
X/ Y 0 1 2
0 2/12 1/12 5/12
1 1/12 1/12 2/12
(a) Determine the probability distribution of X|Y = 0, and E[X|Y = 0].
(b) Determine E[Y ] and E[X].
(c) Determine the probability that Y is larger than zero.
(d) Are X and Y dependent? Justify your answer