Poisson distributions can be derived from the Binomial distribution.
P(E) = f(y,λ) = eλλy
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 GoodnessofFit: the ChiSquare Test
The observed numerical results of an experiment are often compared with those expected
on the basis of some hypothesis.
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 Spring '10
 SmithandDarwiche
 Genetics, Normal Distribution, Probability theory, 10%, 1%, λ

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