Two discrete random variables X and Y have joint pmf given by the following table:

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Y

______________________________________________

| 1 2 3

X | _______________________________

| 1 | 1/12 1/6 C

| 2 | 1/6 1/4 1/12

| 3 | 1/12 1/12 0

[/html]i) Find C

ii) Compute the probability of each of the following events.

a) $\displaystyle X \le 1^{1/2}$

b) X is odd

c) XY is even

d) Y is odd given that X is odd.