Example of Probability
Illustration: It has been determined that the probability density function for the wait in line at a counter is specified by,
In which t is the number of minutes spent waiting in line. Solve each of the following questions concerning to this probability density function.
(a) Prove that this is in fact a probability density function.
(b) Find out the probability that a person will wait in line for at least 6 minutes.
(c) Find out the mean wait in line.
Solution
(a) Prove that this is in fact a probability density function.
This function is evidently positive or zero and so there is not much to do here other than calculate the integral.
Thus it is a probability density function.
(b) Find out the probability that a person will wait in line for at least 6 minutes. The probability that we're searching for here is P (x > 6).
Thus the probability that a person will wait in line for much more than 6 minutes is 54.8811%.
(c) Find out the mean wait in line.
Here is the mean wait time.
Thus, it looks like the average wait time is 10 minutes.