Exercise S1

1. From a group of three republicans, two democrats, and one independent, a committee of two people is to be randomly selected. Let X denote the number of Republicans and Y the number of Democrats on the committee. The table below contains the joint probabilities for X and Y. X Y 0 1 2 _3_3_ 0 0 E 1 1125 if; 0 2 0 0 (A) Find the marginal pmf of X. (B) What is the probability that the independent candidate is selected to be on the commit tee? (C) Find the conditional pmf of X given Y = 0. (D) Are X and Y independent? Justify your