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第165行： − 在概率论和统计学中，泊松分布是以法国数学家西莫恩·德尼·泊松命名的，是一个离散的概率分布，它表示在一个固定的时间段或空间中一定数量的事件的发生概率，这些事件以一个已知的常数平均速率发生，并且独立于与上一个事件的间隔发生时间。'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''还可以用来表示其他有特定间隔的事件数量，如距离、面积或体积。+ 第173行：
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{{Probability distribution
{{Probability distribution
'''<font color="#ff8000"> {概率分布Probability distribution</font>'''
'''<font color="#ff8000"> 概率分布Probability distribution</font>'''
| name = Poisson Distribution
| name = Poisson Distribution
'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''
'''<font color="#ff8000"> 泊松分布 Poisson distribution</font>'''
| type = mass
| type = mass
In probability theory and statistics, the Poisson distribution (; ), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
In probability theory and statistics, the Poisson distribution (; ), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
在概率论和统计学中，'''<font color="#ff8000"> 泊松分布 Poisson distribution</font>'''是以法国数学家西莫恩·德尼·泊松 Siméon Denis Poisson命名的，是一个离散的概率分布，它表示在一个固定的时间段或空间中一定数量的事件的发生概率，这些事件以一个已知的常数平均速率发生，并且独立于与上一个事件的间隔发生时间。还可以用来表示其他有特定间隔的事件数量，如距离、面积或体积。
For instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. Other examples that may follow a Poisson distribution include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source.
For instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. Other examples that may follow a Poisson distribution include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source.
例如，记录每天收到邮件数量的个人可能会注意到，他们平均每天收到4封信。如果收到任何邮件都并不影响未来邮件的到达时间，也就是说，如果不同来源的邮件彼此独立地到达，那么一个合理的假设是，每天收到的邮件数量服从一个'''<font color="#ff8000"> {泊松分布 Poisson distribution</font>'''。其他可能遵循一个'''<font color="#ff8000"> {泊松分布 Poisson distribution</font>'''的例子包括：呼叫中心每小时接到的电话数量和每秒从放射源衰变事件的数量。
例如，记录每天收到邮件数量的个人可能会注意到，他们平均每天收到4封信。如果收到任何邮件都并不影响未来邮件的到达时间，也就是说，如果不同来源的邮件彼此独立地到达，那么一个合理的假设是，每天收到的邮件数量服从一个'''<font color="#ff8000">泊松分布</font>'''。其他可能遵循一个'''<font color="#ff8000">泊松分布</font>'''的例子包括：呼叫中心每小时接到的电话数量和每秒从放射源衰变事件的数量。
The Poisson distribution is popular for modeling the number of times an event occurs in an interval of time or space.
The Poisson distribution is popular for modeling the number of times an event occurs in an interval of time or space.
'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''模型用来模拟一个事件在一段时间或空间内发生的次数。
'''<font color="#ff8000">泊松分布</font>'''模型用来模拟一个事件在一段时间或空间内发生的次数。
A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k = 0, 1, 2, ..., the probability mass function of X is given by:
A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k = 0, 1, 2, ..., the probability mass function of X is given by:
一个离散的随机变量 x 被称为具有参数 > 0的'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''，如果，对于 k = 0,1,2，... ，x 的概率分布函数是:
一个离散的随机变量 x 被称为具有参数 > 0的'''<font color="#ff8000">泊松分布</font>'''，如果，对于 k = 0,1,2，... ，x 的概率分布函数是:
:<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>
:<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>