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.
Give answers with an example table
Marginal distribution of X:
P(X=0) = P((X=0,Y=1) + P((X=0,Y=2) = 1 + 0 = 1
P(X=1) = P((X=1,Y=1) + P((X=1,Y=2) = 0 + 0 = 0
P(X=2) = P((X=2,Y=1) + P((X=2,Y=2) = 0 + 0 = 0
P(X=3) = P((X=3,Y=1) + P((X=3,Y=2) = 0 + 1 = 1
Example table:
X | P(X)
0 | 1
1 | 0
2 | 0
3 | 1
Marginal distribution of Y:
P(Y=1) = P((X=0,Y=1) + P((X=1,Y=1) + P((X=2,Y=1) + P((X=3,Y=1) = 1 + 0 + 0 + 0 = 1
P(Y=2) = P((X=0,Y=2) + P((X=1,Y=2) + P((X=2,Y=2) + P((X=3,Y=2) = 0 + 0 + 0 + 1 = 1
Example table:
Y | P(Y)
1 | 1
2 | 1