Thread: Compute the probability of each

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.

Originally Posted by Stats

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.

i) Use the fact that the total probability has to equal 1.

ii) Identify the favourable events, that is, the favourable combinations of X and Y. Then add up the probability of each favourable event.