Problem 4. Diners arrive at popular restaurant according to a Poisson process N: of rate A. A confused maitre d\" seats the ith diner with probability p, and turns the diner away with probability 1 p. Let Y]; = 1 if the ith diner is seated, and 1/; = 0 otherwise. The number of diners seated up to time t is N: Mt := Z n. i=1 Show that M; is a Poisson random variable and nd its parameter. Assume the Y}- are indepen- dent of each other and the Poisson process