Each customer making a particular Internet purchase must pay with one of three types of credit cards (think Visa, MasterCard, AmEx). Let Ai (i = 1, 2, 3) be the event that a type i credit card is used, with P(A1) = .5, P(A2) = .3, and P(A3) = .2. Suppose that the number of customers who make such a purchase on a given day is a Poisson rv with parameter l. Define rv's X1, X2, X3 by Xi = the number among the N customers who use a type i card (i = 1, 2, 3). Show that these three rv's are independent with Poisson distributions having parameters .5λ, .3λ, and .2λ, respectively.