Week_5_Slides - Stat 2001 Stat 6039 Week 5 • Discrete...

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Unformatted text preview: Stat 2001 / Stat 6039 Week 5 • Discrete Probability Distributions • Mathematical Expectation Guess which distribution this data comes from What about these histograms? Feeling normal? or skewed? How long should you wait? Twins • Poisson introduced this distribution in his research on the Probability of Judgments in Criminal and Civil Matters • The distribution models count data or the number of successes in a unit time interval like the number of accidents in a year or the number of marriages in a month • The underlying assumption is that each count or success are independent of each other and that the rate of counts per unit time interval is constant. • The Poisson distribution is thus the limit of a Binomial distribution. • The Poisson distribution can be used when the constant rate of occurrence is known in a time interval but the probability of a single success occurring in a sub interval is not known. Classic Horse Kick Example • The classic Poisson example is the data set of von Bortkiewicz (1898), for the chance of a Prussian cavalryman being killed by the kick of a horse. • Ten army corps were observed over 20 years, giving a total of 200 observations of one corps for a one year period....
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Week_5_Slides - Stat 2001 Stat 6039 Week 5 • Discrete...

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