The exponential distribution has a characteristic that is called the “memoryless” property. This means P1X 7 x2 = P1X 7 x + x0 X 7 x02. To illustrate this, consider the calls coming into 911. Suppose that the distribution of the time between occurrences has an exponential distribution with a mean of one half hour 1=0.52.

a. Calculate the probability that no calls come in during the first hour.

b. Now suppose that you are monitoring the call frequency, and you note that a call does not come in during the first two hours. Determine the probability that no calls will come in during the next hour.