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Unformatted text preview: ependently, and one at a time into a grid composed of n equal sized cells, what is the probability that a single specified cell contains exactly m points at the conclusion of the experiment?' Because the cells are equal sized the probability that one point falls in the specified cell in a single trial is given by 10 (19)
11 Table 1. Probabilities and frequencies for the hypothetical data set which is the formula for the Poisson distribution. The mean, or expected The variance of the binomial distribution measures the spread of the values the square of the first moment (the mean), and for the binomial distribution the variance is given by (20) (iv) The Poisson distribution as a limit of the binomial In most cases where we wish to apply the binomial in point pattern anal ysis n and r usually have large values, consequently p tends to be small. When n and r are large it can be shown that the Poisson distribution gives very close approximations to the results obtained from the binomial. In fact, the Poisson is a limiting case of the binomial distribution,...
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