Lecture Business statistics in practice (7/e): Chapter 5 - Bowerman, O’Connell, Murphree

Chapter 5 - Discrete random variables. After mastering the material in this chapter, you will be able to: Explain the difference between a discrete random variable and a continuous random variable, find a discrete probability distribution and compute its mean and standard deviation, use the binomial distribution to compute probabilities,...
Nội dung trích xuất từ tài liệu:
Lecture Business statistics in practice (7/e): Chapter 5 - Bowerman, OConnell, Murphree Chapter5 DiscreteRandomVariablesMcGrawHill/Irwin Copyright©2014byTheMcGrawHillCompanies,Inc.Allrightsreserved.DiscreteRandomVariables5.1 TwoTypesofRandomVariables5.2 DiscreteProbabilityDistributions5.3 TheBinomialDistribution5.4 ThePoissonDistribution(Optional)5.5 TheHypergeometricDistribution (Optional)5.6 JointDistributionsandtheCovariance (Optional) 52LO5-1: Explain thedifference between adiscrete random 5.1TwoTypesofRandomVariablesvariable and acontinuous randomvariable.  Randomvariable:avariablethatassumes numericalvaluesthataredeterminedbythe outcomeofanexperiment ◦ Discrete ◦ Continuous  Discreterandomvariable:Possiblevaluescanbe countedorlisted ◦ Thenumberofdefectiveunitsinabatchof20 ◦ Alistenerrating(onascaleof1to5)inanAccuRating musicsurvey  Continuousrandomvariable:Mayassumeany numericalvalueinoneormoreintervals ◦ Thewaitingtimeforacreditcardauthorization ◦ Theinterestratechargedonabusinessloan 53LO5-2: Find a discreteprobability distributionand compute its mean 5.2DiscreteProbabilityDistributionsand standard deviation. Theprobabilitydistributionofadiscrete randomvariableisatable,graphorformula thatgivestheprobabilityassociatedwith eachpossiblevaluethatthevariablecan assume Notation:Denotethevaluesoftherandom variablebyxandthevalue’sassociated probabilitybyp(x) 54LO5-2 DiscreteProbabilityDistributionProperties 1. Foranyvaluexoftherandomvariable, p(x) 0 2. Theprobabilitiesofalltheeventsinthe samplespacemustsumto1,thatis… px 1 all x 55LO5-3: Use the binomialdistribution to computeprobabilities. 5.3TheBinomialDistribution  Thebinomialexperiment characteristics… 1. Experimentconsistsofnidenticaltrials 2. Eachtrialresultsineither“success”or“failure” 3. Probabilityofsuccess,p,isconstantfromtrial totrial  Theprobabilityoffailure,q,is1–p 1. Trialsareindependent  Ifxisthetotalnumberofsuccessesinn trialsofabinomialexperiment,thenxisa binomialrandomvariable 56LO5-3 BinomialDistribution Continued  Forabinomialrandomvariablex,theprobabilityof xsuccessesinntrialsisgivenbythebinomial distribution: n! x n x p x = p q x! n x !  n!isreadas“nfactorial”andn!=n×(n1)×(n2) ×...×1  0!=1  Notdefinedfornegativenumbersorfractions 57LO5-4: Use the Poissondistribution to computeprobabilities (Optional). 5.4ThePoissonDistribution  Considerthenumberoftimesanevent occursoveranintervaloftimeorspace, andassumethat 1. Theprobabilityofoccurrenceisthesamefor anyintervalsofequallength 2. Theoccurrenceinanyintervalisindependentof anoccurrenceinanynonoverlappinginterval  Ifx=thenumberofoccurrencesina specifiedinterval,thenxisaPoiss ...