Find the mean and standard deviation of the waiting time in Example 13.15.

Data from Example 13.15

Two people have agreed to meet in a definite place between six and seven o’clock. Their actual times of arrival are independent and entirely random (no arrival time more likely than any other) within the hour. Find

The density function of the time that the first person arriving has to wait;

The probability that the meeting will occur if the first person to arrive does not wait for longer than 15 minutes.