The memoryless property of the exponential distribution describes the fact that:

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the equations associated with the exponential distribution are so difficult that rarely can anyone remember how to calculate probability without help.

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at any point in time, the exponential random variable forgets or ignores what happened earlier; the future is independent of the past.

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the probability associated with any one span of time is dependent upon the span of time that preceded it.

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the exponential distribution is the only distribution that exhibits an inverse relationship concerning the past. In other words, the more time that precedes an event, the greater the probability of present occurrence.