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limiting case of binomial distribution


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limiting case of binomial distribution is poisson distribution when n is large and p is small
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first start with the pdf of binomial distribution
split up the nCx term
take out the n from each factor collect all the (np) together
eliminate p by changing everything to terms involving n
then take the limit with n -> infinity
you have to use the standard limit that [1-(k/n)]^n -->exp(-k) when n-->infinity
see the following for some steps


answer and  some steps are given below
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limiting case of binomial distribution is poisson
limiting case of binomial distribution is poisson
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