4. Poisson Let Y be the number of customers that arrive at a checkout counter during a given hour (note, Y is the customers per hour). Assuming that Y ~ Poi(/l) is a Poisson random variable with /l = 3. 4a. Write down the probability function pYQy) for Y and clearly specify the values y that Y may take. 4b. During a given hour, What is the probability that at most two customers arrive? 4c. Let Y, =# customers in rst I minutes. We assume Y , ~ Poi(3t/ 60). Find the probability of no customer coming for the rst 15 minutes. That is, nd Pr(A) forA = {Y15 = 0}