00:01
So, to answer the first part or the a part here, in this scenario, we are joining a checkout line with three people ahead of you and the time it takes for cashier to serve each person is exponentially distributed with a mean value of 5 minutes.
00:19
We can model the situation using exponential random variables.
00:23
The sum of these three exponential random variables represents the time it takes for three people ahead of you to be served.
00:31
Since these times are independent, we can calculate the expected waiting time to begin receive service.
00:39
So expected waiting time for one person to be served is 5 minutes.
00:44
So the expected waiting time for three people to be served would be 3 times 5.
00:49
So 15 minutes, that's the answer to the first part.
00:52
Now to answer point b, probability of only one person ahead after waiting 15 minutes.
00:59
So can be written as probability of one person ahead after 15 minutes.
01:11
And this can be modeled as lambda times e power minus lambda t...