Stat 333Basic Probability DistributionsDiscrete Distributionsdistributionprobability mass functionrangeE(X)Var(X)indicator (p)f(0) = 1-p,f(1) =pk=0,1pp(1-p)binomial(n,p)f(k)=±nk²pk(1-p)n-kk,1,...,nnp(1-p)geometric (p)†f(kp(1-p)k-1k=1,2,3,...1p1-pp2neg. binomial(r, p)f(k±k-1r-1²pr(1-p)k-rk=r, r+1rpr(1-p)p2Poisson(λ)f(kλkk!e-λk,1,2λλ†we will always defne the geometric asX= number oF trials up to (and including) the frstSuccess. Similarly we will always defne the negative binomial asXr= number oF trials up to (andincluding) the frstrSuccesses.The indicator, binomial, and Poisson random variables are examples oFcounting variables. Theycount the number oF times a certain eventEoccurs in a fxed number oF trials (indicator andbinomial) or in a fxed time period (Poisson). The geometric and negative binomial are examplesoFwaiting 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.