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# poisson - -m.m x/x Where p(x is the probability that a...

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1Zoo/Psych/Neuro 523 Poisson Distribution This is a statistical law that analyzes the frequency of rather infrequent events (e.g. the number of goals in a soccer match). A famous example of this distribution analyzes the chances that a Prussian cavalryman will be killed by a horsekick. The data come from the records of 20 army corps over a 20 year period. The answer will be expressed as the probability that a corps will have a death in a 1 year period. Let N = total number of samples. In this case N= 200 corps-years Total number of death in the samples = 122 Average number of deaths/corps-year = 122/200 = 0.61 Let’s call this m Poisson’s Law states p(x) = e
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Unformatted text preview: -m .m x /x! Where p(x) is the probability that a sample (one corps-year) will include x events. Applying this to the Prussian cavalry, we get: Expected Observed p = e-m = 0.543 Multiply by N to get n , etc n = 109 109 p 1 = m.e-m = 0.331 n 1 = 66.3 65 p 2 = m 2 /2.e-m = 0.101 n 2 = 20.2 22 p 3 = m 3 /6.e-m = 0.021 n 3 = 4.1 3 p 4 = m 4 /24.e-m = 0.003 n 4 = 0.6 1 Pretty good agreement. For the neuromuscular junction, the each stimulus to the nerve provides a sample. We analyze the number of responses in which we get an event the same size as 1 mepp, the same size as 2 mepp’s, 3 mepp’s, etc....
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