The exponential distribution has a characteristic that is called the “memory less” property. This means P (X > x) = P (X > x + x0 | X > x0). 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 (= 0.5).
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.