A certain public television station needs money badly and runs a fund-raising TV entertainnn'nit program. Assume that pledges arrive by phone according to a Poisson process, with intensity 2 pledges per minute during the one-hour length of the program. (a) Determine the probability that there are no pledges in a 3-minute period. (1)) Suppose the hourlong program is divided into 20 intervals each of length 3 minutes. Give an expression for the probability that exactly y of these intervals receive no pledges. (e) If each pledge is worth $20, nd the expected value and the variance of the total amount of the pledges over the 60 minute program? ((1) Using R, run a simulation of the amount received in a one hour program. Repeat this 100000 times and (mnpare the relative frtxlnency that the total annlnt pledged exceeds $3000 with the probability of this event. (you may use rpois)