Question

Karin arrives at the post office, which opens at 9:00 a.m., at 9:05 a.m. She finds two cashiers at work, both serving one customer each. The customers started being served at 9:00 and 9:01, respectively. The service times are independent and Exp(8)-distributed. Let Tk be the time from 9:05 until service has been completed for k of the two customers, k = 1, 2. Find ETk for k=1 and 2.

The answer is ET1 =4, ET2 =12.

Answer 1

The solution is given below. The source of the confusion might be that the parameter for the exponential distribution might mean different things in different books. In most cases, including Wikipedia at the moment, it is the inverse of the expected value. However, in this case it means the expected value itself. Hence the answers come out to be 4 and 12 respectively. The proof itself follows from the definitions of conditional probability and the exponential distribution. I have also used the fact that density function can be gotten from distribution function by differentiating. I hope it's all clear.