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In probability and statistics, memorylessness is a property of certain probability distributions: the exponential distributions of non-negative real numbers and the geometric distributions of non-negative integers. The property is most easily explained in terms of "waiting times." Suppose that a random variable, ''X'', is defined to be the time elapsed in a shop from 9 am on a certain day until the arrival of the first customer: thus ''X'' is the time a server ''waits'' for the first customer. The "memoryless" property makes a comparison between the probability distributions of the time a server has to wait from 9 am onwards for his first customer, and the time that the server still has to wait for the first customer on those occasions when no customer has arrived by any given later time: the property of memorylessness is that these distributions of "time from now to the next customer" are exactly the same. As another example, suppose ''X'' is the lifetime of a car engine given in terms of number of miles driven. If the engine has lasted 200,000 miles, then, based on our intuition, it is clear that the probability that the engine lasts another 100,000 miles is not the same as the engine lasting 100,000 miles from the first time it was built. However, memorylessness states that the two probabilities are the same. In essence, we 'forget' what state the car is in. In other words, the probabilities are not influenced by how much time has elapsed. The terms "memoryless" and "memorylessness" are used in a very different way to refer to Markov processes in which the underlying assumption of the Markov property implies that the properties of random variables related to the future depend only on relevant information about the current time, not on information from further in the past. The present article describes the use outside the Markov property, limited to conditional probability distributions. ==Discrete memorylessness== Suppose ''X'' is a discrete random variable whose values lie in the set . The probability distribution of ''X'' is memoryless precisely if for any ''m'', ''n'' in , we have : Here, Pr(''X'' > ''m'' + ''n'' | ''X'' > ''m'') denotes the conditional probability that the value of ''X'' is larger than ''m'' + ''n'', given that it is larger than or equal to ''m''. The ''only'' memoryless discrete probability distributions are the geometric distributions, which feature the number of independent Bernoulli trials needed to get one "success," with a fixed probability ''p'' of "success" on each trial. In other words those are the distributions of waiting time in a Bernoulli process. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Memorylessness」の詳細全文を読む スポンサード リンク
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