1.

(10 points) Suppose that you are interviewing for a job that has a total of n applicants. After your interview you conclude that the employers have a system that ranks the candidates from 1 to n. (a) If X is the rank of a randomly selected candidate, what is the probability mass function of X? (3 points) (b) Compute the expected rank of a randomly selected candidate. (3 points) (c) Compute the variance associated with this random variable. (4 points)9 points) Consider a deck consisting of 5 cards, marked 1,2,..,5. Three of these cards are selected at random. Define a random variable, X, by X = the sum of the resulting numbers. (a) Compute the pmf of X. (6 points) (b) Compute E(X). (2 points) (c) Compute Var(X). (2 points)