Each member of a population of size n is, independently, female with probability or male with probability 1 - p. Let X be the number of the other n - 1 members of the population that are the same sex as is person 1. (So X = n - 1 if all people are of the same sex.)

a. Find P(X = i), i = 0, ..., n - 1.

Now suppose that two people of the same sex will, independently of other pairs, be friends with probability α; whereas two persons of opposite sexes will be friends with probability β. Find the probability mass function of the number of friends of person 1.