如何用英语简单解释泊松分布和指数分？

    如果单位时间发生的次数（如到达的人数）服从参数为r的泊松分布，则任连续发生的两次时间的间隔时间序列服从参数为r的指数分布 If the number of times per unit time (such as the number of arrival) obey the parameters for the distribution of R Poisson, time interval sequence is as two times consecutively obey the parameters for the distribution of R index 双语对照。
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    泊松分布与指数分布 Poisson distribution and exponential distribution 假设一事件在任何长为t的时间内出现故障的次数v(t)服从参数为it的泊松分布，则相邻两次事件的时间间隔T服从参数为i的指数分布。
   Suppose that a failure in any event for t long time v (T) to the number of parameters for the distribution of it Poisson, is adjacent to the two event time interval T obeys the parameters for the distribution of I index。
     解释： Interpretation: 直接从泊松分布解释比较困难。因为泊松分布是二项分布在一定条件下的近似，所以我们看二项分布。 Directly from the Poisson distribution to explain difficult。
   Because the Poisson distribution are the two distribution in a certain approximation, we look at two distribution。
     设事件发生概率为p，则不发生概率为1-p。所谓“相邻两次事件”，即“在这两次事件之间没有发生事件”。 Set event probability for the P, not the probability for the 1-p。
   The so-called "two adjacent event", namely "no events between the two events"。   按二项分布近似到泊松分布的过程，将相邻两次事件之间的时间间隔T分割为很多个小时间段，每段时长为λ，在每个小时间段内发生一次事件的概率为p，不发生概率为1-p。
   According to the two distribution approximation to the Poisson distribution, will be between two adjacent event time interval T is divided into many small time, each time length λ, an event probability in each time period is p, not the probability for the 1-p 若在时间点t上发生了一次事件，那么： If the t at a time there was an event, then: 在t与t+λ之间没有发生事件的概率为1-p，在t+λ与t+2λ之间发生了事件的概率为p，两次事件之间时间间隔为λ的概率为(1-p)p； Probability events did not occur between T and t+ λ 1-p, the probability of events between t+ λ t+2 λ P and probability, the time interval between two events for lambda for (1-p) 在t与t+2λ之间没有发生事件的概率为(1-p)2，在t+2λ与t+3λ之间发生了事件的概率为p，两次事件之间时间间隔为2λ的概率为(1-p)2p； Probability events did not occur between T and t+2 λ (1-p) is 2, the probability of events between t+2 λ and t+3 λ P, between the two event time interval for the probability of 2 λ (1-p) for …… 。
    。。。。。 嗯，这个就有点像指数分布了。 Well, this is a bit like the exponential distribution。