ProbabilityDistributions

ProbabilityDistributions - Stat 333 Basic Probability...

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Stat 333 Basic Probability Distributions Discrete Distributions distribution probability mass function range E( X ) Var( X ) indicator ( p ) f (0) = 1 - p , f (1) = pk =0 , 1 pp (1 - p ) binomial( n,p ) f ( k )= ± n k ² p k (1 - p ) n - k k , 1 ,...,n np (1 - p ) geometric ( p ) f ( k p (1 - p ) k - 1 k =1 , 2 , 3 ,... 1 p 1 - p p 2 neg. binomial( r, p ) f ( k ± k - 1 r - 1 ² p r (1 - p ) k - r k = r, r +1 r p r (1 - p ) p 2 Poisson( λ ) f ( k λ k k ! e - λ k , 1 , 2 λ λ we will always defne the geometric as X = number oF trials up to (and including) the frst Success. Similarly we will always defne the negative binomial as X r = number oF trials up to (and including) the frst r Successes. The indicator, binomial, and Poisson random variables are examples oF counting variables . They count the number oF times a certain event E occurs in a fxed number oF trials (indicator and binomial) or in a fxed time period (Poisson). The geometric and negative binomial are examples oF waiting time variables . They count the number oF trials (the waiting time) required to obtain a
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This note was uploaded on 08/01/2008 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.

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