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

[html]

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)

b) X is odd

c) XY is even

d) Y is odd given that X is odd.