week5 - Relation between Binomial and Poisson Distributions...

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week 5 1 Relation between Binomial and Poisson Distributions Binomial distribution Model for number of success in n trails where P (success in any one trail) = p . Poisson distribution is used to model rare occurrences that occur on average at rate λ per time interval. Can think of “rare” occurrence in terms of p Æ 0 and n Æ . Take these limits so that λ = np . So we have that
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week 5 2 Continuous Probability Spaces is not countable. Outcomes can be any real number or part of an interval of R , e.g. heights, weights and lifetimes. Can not assign probabilities to each outcome and add them for events. Define as an interval that is a subset of R . F – the event space elements are formed by taking a (countable) number of intersections, unions and complements of sub-intervals of . Example: = [0,1] and F = { A = [0,1/2), B = [1/2, 1], Φ , }
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week 5 3 How to define P ? Idea - P should be weighted by the length of the intervals. - must have P ( ) = 1 - assign 0 probability to intervals not of interest.
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This note was uploaded on 09/22/2010 for the course STATISTICS STA257 taught by Professor Mcdunnough during the Fall '10 term at University of Toronto- Toronto.

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week5 - Relation between Binomial and Poisson Distributions...

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