Discrete Probability Distributions ppt课件

发布时间:2014-01-31

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简略标题:Discrete Probability Distributions

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Discrete Probability Distributions ppt课件内容预览:Distinguish between discrete and continuous random variables.Differentiate between the binomial and the Poisson discrete probability distributions and their applications.Construct a probability distribution for a discrete random variable,determine its mean and variance,and specify the probability that a discrete random variable will have a given value or value in a given range.Chapter 6- KeyTermsRandom variablesDiscreteContinuousBernoulli processProbability distributionsBinomial distributionPoisson distributionDiscrete vs ContinuousVariablesDiscrete Variables: Can take on only certain values along an intervalthe number of sales made in a weekthe volume of milk bought at a storethe number of defective partspptContinuous Variables: Can take on any value at any point along an intervalthe depth at which a drilling team strikes oilthe volume of milk produced by a cowthe proportion of defective partsDescribing the Distribution for a Discrete RandomVariableThe probability distribution for a discrete random variable defines the probability of a discrete value x.Mean: μ= E(x)=Variance: s2= E[(x –μ)2]=The Bernoulli Process,CharacteristicsThere are two or more consecutive trials.In each trial,there are just two possible outcomes.The trials are statistically independent.The probability of success remains constant trial-to-trial.The BinomialDistributionThe binomial probability distribution defines the probability of exactly x successes in n trials of the Bernoulli process.for each value of x.Mean: μ= E(x)=n pVariance: s2= E[(x –μ)2]=n p (1– p)The Binomial Distribution,An Example Worked byEquationProblem 6.23: A study by the International Coffee Association found that 5216036160f the U.S.population aged 10and over drink coffee. For a randomly selected group of 4individuals,what is the probability that 3of them are coffee drinkers? NumberProportionCoffee drinkers (x)3 .52Noncoffee drinkers 1 .48Totals 41.00So,p =0.52,(1– p)=0.48,x =3,(n – x)=1.The Binomial Distribution,Working with theEquationTo solve the problem,we substitute:The Binomial Distribution,An Example Worked withTablesProblem: According to a corporate association,50.020100240f the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents,with x =the number sampled who were boating participants that year,determine:a. E(x)=n p =20x 0.50=10b. P(x £8) Go to Appendix, Table A.2,n =20. For p =0.5and k =8, P(x £8)=0.2517c. P(x =10) Go to Appendix, Table A.1,n =20. For p =0.5and k =10, P(x =10)=0.1762Example: BinomialTablesProblem : According to a corporate association,50.0473f the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents,with x =the number sampled who were boating participants that year,determine:d. P(x =12) Go to Appendix, Table A.1,n =20. For p =0.5and k =12, P(x =12)=0.1201e. P(7£x £13) Go to Appendix, Table A.2,n =20. For p =0.5
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