The probability density function of the time you arrive at a terminal (in minutes after 8:00 a.m.) is f (x) = 0.1 exp(− 0.1x) for 0 < x. Determine the probability that

(a) You arrive by 9:00 a.m.

(b) You arrive between 8:15 a.m. and 8:30 a.m.

(c) You arrive before 8:40 a.m. on two or more days of five days. Assume that your arrival times on different days are independent.

(d) Determine the cumulative distribution function and use the cumulative distribution function to determine the probability that you arrive between 8:15 a.m. and 8:30 a.m.