The number of people that enter a drugstore in a given hour is a Poisson random variable with parameter 2 = 10. Let M and W represent the number of men and women, respectively, that enter the store in a given hour. (Assume that each new customer is equally likely to be a man or a woman.) (a) Find the joint probability mass function of M and W. That is, find a formula for p(i, j) = P(M = i, W = j). (Hint: First write ple, j) = P(M = 2,W=;) = P(M = 1, M +W = i +1) and then compute the term on the right-hand side by using the conditional probability formula P(An B) = P(A|B)P(B).)
(b) Compute the conditional probability that at most 3 men entered the drug- store, given that 10 women entered in that hour.