joint pmf and marginal pmf?

Question

the join pmf of n X n Y is f(x,y)=1/6 0<=X+Y<=2. where X and Y are integer.

(a) skecth the support of X and Y.
(b) find the marginal pmf of f(x) and f(y).

Answer 1

There's an additional assumption required to make this work, namely that X >= 0 and Y >= 0.

Given this additional restriction, the support of X and Y is simply the set of ordered pairs {(0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (0, 2)}.

The marginal PMFs of X and Y are the same, which you can see by symmetry. They are given by
n f_x(n)
0 1/2
1 1/3
2 1/6

Note that the marginal pmf for a particular value is just the sum of the individual probabilities corresponding to it. So, for instance, the marginal pmf for X at 0 is
f(0, 0) + f(0, 1) + f(0, 2)
= 1/6 + 1/6 + 1/6
= 1/2.

Answer 2

dwef4v