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Just a note

These are Poisson distributions for a mean expected frequency of 0.3, 1 3, 9 and 27. Note that the larger the mean, the closer the distribution approximates to the normal distribution.

Remember that although the expected frequency is Pn under the binomial model, under the Poisson model the sample size (n) is undefined, and often in practice the number of zeros is unknown - but is assumed to be much larger than the frequency of ones. This model therefore assumes the frequency of ones, f, is an unbiased estimate of λ - which is equivalent to Pn.