The waiting time for an incoming call at the front desk of mathematics Department follows an exponential distribution. During business hours, the average of the waiting times is 10 minutes.

(a)  What is the cumulative distribution function and the variance of the waiting time?

(b)  What is the probability that the first call after 9:30 a.m. is between 9:45 a.m. and 9:55 a.m.?

(c)   If there is no call between 9:30 a.m. and 9:45 a.m., what is the probability that there will be no call between 9:30 a.m. and 9:55 a.m.?