I. Problem I: X is a Poisson H. with rate of 15 per hour. following the Poisson an'ival process. to) Find the probabilityr of no anivals during a 15 hour interval (b) Find the pranolss'nilit}.r of X 3:- 3 arrivals in 4 hours to] Find the average interarrivat time. (d) For an interval of 2 hours. let A = { :- X 3::- 3}. B = {5 if. I 5 9}. then nd Pr( e': X 6.: 11|A.E] to) Find EUL'IA n B) in the previous problem. {f} If Y = exp{2X}. then nd E{Y|A U E]. [3] Find EWEIA n B} on Find vsrwm n o}