Problem 2. Assume each person is color-blind with the probability. There are 5 subjects participating in a research project on color blindness. Let X denote the random variable that takes the number of color-blind subjects among them. (a) Find the probability mass function of X. (b) Find the cumulative distribution function of X. (c) Find E[X]. (d) Find Var(X). Problem 3. A random variable X represents the number of patients arriving in an emergency room within a day. X is a Poisson random variable with the rate = 10 when it does not rain, i.e., 10 Pr(X | A) e 10% i! " i = 0, 1, 2,..., where A is the event of "not raining." For rainy days, however, the rate (Poisson parameter) is increased to = 20. The probability that it rains each day is 0.1, i.e., Pr(A) = 1. (a) Find the PMF of X. Is X a Poisson r.v.? (b) What is the probability for a day to be rainy if X = 15 that day? 10