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Poisson distributions can be derived from the Binomial distribution

# Poisson distributions can be derived from the Binomial distribution

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Poisson distributions can be derived from the Binomial distribution. P(E) = f(y,λ) = e-λλy y! • P(E) = the probability that there will be y successes • e = base of natural logarithm • y = the number of successes, the probability of which is calculated by the function for each y of interest, y = 0, 1, 2, 3... • λ = the expected number of occurrences during the given interval, a positive real number An example: The Poisson distribution allows us to calculate the probability that k individuals would have a desired genotype in a generation. What is the likelihood of finding precisely 6 desired offspring when the average frequency is only 1% and 400 offspring are examined? Since 1% of 400 = 4, λ = 4, y is 6, the probability is about 10%. Figure 1.2 Poisson Distribution for λ = 1, 4, and 10 Poisson distributions for λ = 1, 4, and 10 y = number of events expected frequency Lab Topic 1 9 4. Determining Goodness-of-Fit: the Chi-Square Test The observed numerical results of an experiment are often compared with those expected on the basis of some hypothesis.

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