A doctor has scheduled two appointments, one at 1pm and theother at 1:30pm. The amount of time the doctor spends with thepatient is a constant 20 minutes plus a random amount of time whichis distributed as exponential with mean 8 minutes. Assume that bothpatients will be on time for their appointments.
- What is the chance the doctor will be late for her 1:30appointment because she spends more than 30 minutes with her 1pmappointment?
- On average, how long will the 1:30 appointment be at thedoctor’s office?
The time the 1:30 appointment spendsin the office is the sum of 3 parts: the random waiting time W, theconstant 20 minutes of examination time and the additional randomexamination time T.
We seek E[W + 20 + T] = E[W] + 20 +E[T]
To determine the E[W], condition onwhether or not the 1:00pm appointment is still going on at1:30pm.
Explanations with answers please
