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1.9 The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown to be given by the binomial distribution Consider a situation where the probability p is small (p « 1) and where one is interested in the case n < N. (Note that if N is large, W(n) becomes very small if n → N because of the smallness of the factor P when p 《I. Hence W(n) is indeed only appreciable when n« N.) Several approximations can then be made to reduce (1) to simpler form.
(c) Hence show that (1) reduces to 7- where λ·NP is the mean number of events. Poisson distribution. The distribution (2) is called the
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