The values of X are 0,1, 2,3 and Y are 1,2.
Write down tables for the marginal distribution of X and of Y, i.e. give the values of
Ρ = ( X x) for all x , and of Ρ = (Y y) for all y .
Marginal distribution of X:
P(X=0) = P(0,1) + P(0,2) = 0 + 0 = 0
P(X=1) = P(1,1) + P(1,2) = 0 + 0 = 0
P(X=2) = P(2,1) + P(2,2) = 0 + 0 = 0
P(X=3) = P(3,1) + P(3,2) = 0 + 0 = 0
Marginal distribution of Y:
P(Y=1) = P(0,1) + P(1,1) + P(2,1) + P(3,1) = 0 + 0 + 0 + 0 = 0
P(Y=2) = P(0,2) + P(1,2) + P(2,2) + P(3,2) = 0 + 0 + 0 + 0 = 0
Therefore, the marginal distribution of X and Y are both 0 for all values of x and y.