A store has N clients per day, where the probability that N willbe three is 0.1, that N will be two is 0.4, that N will be one is0.3. The store never gets more than three clients per day.
(a) Is N binomial? Poisson?
(b) Write the cumulative distribution function for N.
(c) What is the average number of clients per day?
(d) You want to study how many bags of milk each client buys.Half of them buy two bags, a quarter buy 1 bag, and the rest buynone. Let X be the number of bags of milk purchased on a given day.Are X and N independent?
(e) What is the probability that 5 bags will be purchased?
(f) What is the probability that there will be 3 clients andthat 5 bags will be purchased?
(g) What is the probability the 5 bags will be purchased giventhat there are three clients?
(h) Find the probability function of X.
