00:01
First, let's write what the variables represent, starting with w is going to be the time the second patient spurs on the office, and x is going to be the time the first patient spends on the doctor's office.
00:21
If we write the distribution for w, we have a piecewise function saying, x which is a time the first patient spends at the doctor minus 30 if the first patient spends more than 30 minutes because if the first patient spends let's say 35 minutes and 35 minus 30 the second patient is going to be five minutes waiting if the first patient spends let's say 40 minutes at the doctor's office, then the second patient is going to be 40 minus 30 is going to be 10 minutes waiting.
01:03
Otherwise, that means if the first patient spends less than 30 minutes, or even if the first patient doesn't show up, then the second patient is not going to spend any time waiting at the doctor's office.
01:18
It's just going to spend the 30 minutes that the doctors take to take care of him.
01:25
Or however time the doctor takes to attend him.
01:29
Then the formula for the expected time that the second patient is going to be at the doctor's office.
01:35
That means the waiting time plus the time the doctor's takes checking the second patient is going to be equal to the waiting time.
01:44
We call it ew because it's going to be expected waiting time plus 30 minutes because that's the mean time the doctor takes checking the second patient.
01:56
Is stated on the problem.
01:58
We now have to define this expected waiting time for the second patient.
02:03
This is an exponential random variable as the problem states...