00:01
For this question, we are told that a shuttle train completes a journey from an airport to a nearby city and back every 15 minutes.
00:10
For part a, we consider that the waiting time as a uniform distribution, and we're asked for the probability that a passenger has to wait more than six minutes for a shuttle train.
00:21
So if the round trip is 15 minutes and the waiting time is uniform, the amount of time that you have to wait, let's call that random variable x, is uniformly distributed.
00:33
On the time interval from 0 to 15 minutes.
00:38
For part a, we want the probability that x is more than 6.
00:43
This can be expressed as 1 minus the probability that the waiting time is at most 6 minutes.
00:51
Now, for a continuous uniform random variable, such as this one, the cumulative distribution function, f of x, is given by this formula.
01:15
Here, a is the lower end of the interval, and b is the upper end of the interval.
01:20
So for this particular random variable, cumulative distribution function is x over 15.
01:34
So the probability that x is at most 6 is the cdf evaluated at 6...