Compute a PX2 l Y3 and b PY3 l X3 for the following joint di

Compute (a) P(X=2 l Y=3) and (b) P(Y=3 l X=3) for the following joint distribution:

Y X=1 2 3

1 0.2 0.15 0.05

2 0.10 0 0.10

3 0.05 0.15 0.20

Hint: solution

Y X=1 2 3

1 1/9 2/9 1/3

2 1/18 0 1/6

3 0 1/9 0

(a) P(X=2 l Y=3)

=P(X=2 and Y=3)/P(Y=3)

=0.15/(0.05+0.15+0.20)

=0.375

(b) P(X=3 l Y=3)

=P(X=3 and Y=3)/P(Y=3)

=0.20/(0.05+0.15+0.20)

=0.5