5. 10 pt A survey shows that the number of customers arriving at the Subway restaurant on University Drive between 12:00 PM and 1:00 PM on any given day can be modeled by a Poisson random variable N with parameter A. A more detailed study shdws that, eaeh customer orders a sandwich, with probability 3}, or orders a pizza with probability 1 p, independently from other customers. Let X be the number of customers who order sandwich, and Y be the number of customers who order pizza, between 12:00 PM and 1:00 PM. (a) 4 pt Find the joint PMF of X and Y. (b) 4 pt Find the PMF of X and the PMF of Y (using the result of (a)). (c) 2 pt Find the mean and the variance of X and the mean and the variance of Y