2. 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 shows that each customer orders a sandwich with probability p, 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) 2 pt Are X and Y independent? Justify your answer. (b) 2 pt Find the conditional mean and variance of X given that N : 10. (c) 6 pt Find the conditional mean and variance of X given that N > 0