![]() ![]() ![]() P ( X > r + t | X > r) = P ( X > t) for all r ≥ 0 and t ≥ 0įor example, if five minutes have elapsed since the last customer arrived, then the probability that more than one minute will elapse before the next customer arrives is computed by using r = 5 and t = 1 in the foregoing equation. Specifically, the memoryless property says that The exponential and geometric probability density functions are the only probability functions that have the memoryless property. This is referred to as the memoryless property. With the exponential distribution, this is not the case–the additional time spent waiting for the next customer does not depend on how much time has already elapsed since the last customer. Since an unusually long amount of time has now elapsed, it would seem to be more likely for a customer to arrive within the next minute. Suppose that five minutes have elapsed since the last customer arrived. Recall that the amount of time between customers for the postal clerk discussed earlier is exponentially distributed with a mean of two minutes. Memorylessness of the Exponential Distribution It also assumes that the flow of customers does not change throughout the day, which is not valid if some times of the day are busier than others.
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