1. A joint probability mass function is given by

P(X=1,Y=1)=1/8, P(X=1,Y=2)=1/4

P(X=2,Y=1)=1/8, P(X=2,Y=2)=1/2.

(a) Find the marginal distributions of X and Y.

(b) Are X and Y independent? (c) Compute P(XY 3). (d) Compute P(X + Y > 2).

2. A bag contains r red and g green candies. We draw n candies from the bag without replacement. Find the expected number of red candies drawn by using indicator variables.