商务统计学英文版教学课件第5章.ppt
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1、Discrete Probability DistributionsChapter 5ObjectivesIn this chapter,you learn:nThe properties of a probability distribution.nTo compute the expected value and variance of a probability distribution.nTo compute probabilities from binomial,and Poisson distributions.nTo use the binomial,and Poisson di
2、stributions to solve business problemsDefinitionsnDiscrete variables produce outcomes that come from a counting process(e.g.number of classes you are taking).nContinuous variables produce outcomes that come from a measurement(e.g.your annual salary,or your weight).Types Of VariablesCh.5Ch.6Ch.5Ch.6T
3、ypes Of VariablesDiscrete VariableContinuousVariableCh.5Ch.6Discrete VariablesnCan only assume a countable number of valuesExamples:nRoll a die twiceLet X be the number of times 4 occurs(then X could be 0,1,or 2 times)nToss a coin 5 times.Let X be the number of heads (then X =0,1,2,3,4,or 5)Probabil
4、ity Distribution For A Discrete VariablenA probability distribution for a discrete variable is a mutually exclusive listing of all possible numerical outcomes for that variable and a probability of occurrence associated with each outcome.Interruptions Per Day In Computer NetworkProbability00.3510.25
5、20.2030.1040.0550.05Probability Distributions Are Often Represented GraphicallyP(X)0.40.30.20.1012345XDiscrete Variables Expected Value(Measuring Center)n Expected Value(or mean)of a discrete variable(Weighted Average)NiiixXPx1)(E(X)Interruptions Per Day In Computer Network(xi)ProbabilityP(X=xi)xiP(
6、X=xi)00.35(0)(0.35)=0.0010.25(1)(0.25)=0.2520.20(2)(0.20)=0.4030.10(3)(0.10)=0.3040.05(4)(0.05)=0.2050.05(5)(0.05)=0.251.00=E(X)=1.40nVariance of a discrete variablenStandard Deviation of a discrete variablewhere:E(X)=Expected value of the discrete variable X xi =the ith outcome of XP(X=xi)=Probabil
7、ity of the ith occurrence of XDiscrete Variables:Measuring Dispersion N1ii2i)xP(XE(X)x2 N1ii2i)xP(XE(X)x2Discrete Variables:Measuring Dispersion(continued)Interruptions Per Day In Computer Network(xi)ProbabilityP(X=xi)xi E(X)2xi E(X)2P(X=xi)00.35(0 1.4)2 =1.96 (1.96)(0.35)=0.68610.25(1 1.4)2 =0.16 (
8、0.16)(0.25)=0.04020.20(2 1.4)2 =0.36 (0.36)(0.20)=0.07230.10(3 1.4)2 =2.56 (2.56)(0.10)=0.25640.05(4 1.4)2 =6.76 (6.76)(0.05)=0.33850.05(5 1.4)2 =12.96(12.96)(0.05)=0.6482=2.04,=1.4283 N1ii2i)xP(XE(X)xProbability DistributionsContinuous Probability DistributionsBinomialPoissonProbability Distributio
9、nsDiscrete Probability DistributionsNormalCh.5Ch.6Binomial Probability DistributionnA fixed number of observations,nne.g.,15 tosses of a coin;ten light bulbs taken from a warehousenEach observation is categorized as to whether or not the“event of interest”occurredne.g.,head or tail in each toss of a
10、 coin;defective or not defective light bulbnSince these two categories are mutually exclusive and collectively exhaustivenWhen the probability of the event of interest is represented as,then the probability of the event of interest not occurring is 1-nConstant probability for the event of interest o
11、ccurring()for each observationnProbability of getting a tail is the same each time we toss the coinBinomial Probability Distribution(continued)nObservations are independentnThe outcome of one observation does not affect the outcome of the othernTwo sampling methods deliver independencenInfinite popu
12、lation without replacementnFinite population with replacementPossible Applications for the Binomial DistributionnA manufacturing plant labels items as either defective or acceptablenA firm bidding for contracts will either get a contract or notnA marketing research firm receives survey responses of“
13、yes I will buy”or“no I will not”nNew job applicants either accept the offer or reject itThe Binomial DistributionCounting TechniquesnSuppose the event of interest is obtaining heads on the toss of a fair coin.You are to toss the coin three times.In how many ways can you get two heads?nPossible ways:
14、HHT,HTH,THH,so there are three ways you can getting two heads.nThis situation is fairly simple.We need to be able to count the number of ways for more complicated situations.Counting TechniquesRule of CombinationsnThe number of combinations of selecting x objects out of n objects isx)!(nx!n!Cxn wher
15、e:n!=(n)(n-1)(n-2).(2)(1)x!=(X)(X-1)(X-2).(2)(1)0!=1 (by definition)Counting TechniquesRule of CombinationsnHow many possible 3 scoop combinations could you create at an ice cream parlor if you have 31 flavors to select from and no flavor can be used more than once in the 3 scoops?nThe total choices
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