Class 05 Discrete probability models

Class 05 Discrete probability models - Models of discrete...

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T. R. Willemain MAU Spring 06 1 Models of discrete random variables
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T. R. Willemain MAU Spring 06 2 Agenda PMF and CDF of discrete RVs Expectations of discrete random variables Frequently used models of discrete random variables In-class exercises Microquiz 05
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T. R. Willemain MAU Spring 06 3 PMF and CDF
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T. R. Willemain MAU Spring 06 4 PMF and CDF
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T. R. Willemain MAU Spring 06 5 Mean and Variance
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T. R. Willemain MAU Spring 06 6 Frequently used models Bernoulli : 0 or 1; models “coin flip” type situations Binomial : 0, 1… n; models “total # of heads in n flips” Poisson : 0, 1, 2, … ∞; models count of purely random events in fixed interval, e.g., # of emergencies in a day, # of cracks in 1 mile of sidewalk
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T. R. Willemain MAU Spring 06 7 Bernoulli model Possible outcomes are binary: X = 0 or 1 live/die, work/fail, heads/tails Successive trials are “independent” i.e., what happens in one has no influence on next Constant probability of success P(X=1) = p so P(X=0) = 1-p Expectations E[X] = p V[X] = p(1-p)
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T. R. Willemain MAU Spring 06 8 Binomial model
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T. R. Willemain MAU Spring 06 9 Risk Analysis of Tile Loss on the Space Shuttle
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T. R. Willemain MAU Spring 06 10 Map of risk zones
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T. R. Willemain MAU Spring 06 11 A binomial submodel for # of patches of tile loss
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T. R. Willemain MAU Spring 06 12 Poisson model
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T. R. Willemain MAU Spring 06
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Class 05 Discrete probability models - Models of discrete...

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