【導(dǎo)讀】UseBayes?ElementaryEvent–themostbasicoute. Elementaryevent–Anoutefromasample. ContingencyTables. TreeDiagrams. IfE1occurs,thenE2cannotoccur. thesametime.IndependentEvents. thefirstflip.DependentEvents

　　

【正文】 463 Using Poisson Tables X ?t 0 1 2 3 4 5 6 7 Example: Find P(x = 2) if ? = .05 and t = 100 . 0 7 5 82! e(0 . 5 0 )!x e)t()2x(P0 . 5 02tx????????Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 464 Graph of Poisson Probabilities 0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 00 . 5 00 . 6 00 . 7 00 1 2 3 4 5 6 7xP(x) X ?t = 0 1 2 3 4 5 6 7 P(x = 2) = .0758 Graphically: ? = .05 and t = 100 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 465 Poisson Distribution Shape ? The shape of the Poisson Distribution depends on the parameters ? and t: 0 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 51 2 3 4 5 6 7 8 9 10 11 12xP(x)0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 00 . 5 00 . 6 00 . 7 00 1 2 3 4 5 6 7xP(x)?t = ?t = Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 466 The Hypergeometric Distribution Binomial Poisson Probability Distributions Discrete Probability Distributions Hypergeometric Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 467 The Hypergeometric Distribution ? “ n” trials in a sample taken from a finite population of size N ? Sample taken without replacement ? Trials are dependent ? Concerned with finding the probability of “x” successes in the sample where there are “X” successes in the population Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 468 Hypergeometric Distribution Formula NnXxXNxnCCC)x(P???. Where N = Population size X = number of successes in the population n = sample size x = number of successes in the sample n – x = number of failures in the sample (Two possible outes per trial) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 469 Hypergeometric Distribution Formula 0 . 31 2 0(6 )(6 )CCCCCC2)P(x1034261NnXxXNxn ???????■ Example: 3 Light bulbs were selected from 10. Of the 10 there were 4 defective. What is the probability that 2 of the 3 selected are defective? N = 10 n = 3 X = 4 x = 2 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 470 Hypergeometric Distribution in PHStat ? Select: PHStat / Probability amp。 Prob. Distributions / Hypergeometric … Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 471 Hypergeometric Distribution in PHStat ? Complete dialog box entries and get output … N = 10 n = 3 X = 4 x = 2 P(x = 2) = (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 472 The Normal Distribution Continuous Probability Distributions Probability Distributions Normal Uniform Exponential Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 473 The Normal Distribution ? ‘ Bell Shaped’ ? Symmetrical ? Mean, Median and Mode are Equal Location is determined by the mean, μ Spread is determined by the standard deviation, σ The random variable has an infinite theoretical range: + ? to ? ? Mean = Median = Mode x f(x) μ σ Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 474 By varying the parameters μ and σ, we obtain different normal distributions Many Normal Distributions Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 475 The Normal Distribution Shape x f(x) μ σ Changing μ shifts the distribution left or right. Changing σ increases or decreases the spread. Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 476 Finding Normal Probabilities Probability is the area under the curve! a b x f(x) P a x b ( ) ? ? Probability is measured by the area under the curve Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 477 f(x) x μ Probability as Area Under the Curve The total area under the curve is , and the curve is symmetric, so half is above the mean, half is below 1 . 0)xP( ??????0 . 5)xP( μ ????0 . 5μ)xP( ?????Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 478 Empirical Rules μ 177。 1σ encloses about 68% of x’s f(x) x μ μ?1σ μ?1σ What can we say about the distribution of values around the mean? There are some general rules: σ σ % Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 479 The Empirical Rule ? μ 177。 2σ covers about 95% of x’s ? μ 177。 3σ covers about % of x’s x μ 2σ 2σ x μ 3σ 3σ % % (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 480 Importance of the Rule ? If a value is about 2 or more standard deviations away from the mean in a normal distribution, then it is far from the mean ? The chance that a value that far or farther away from the mean is highly unlikely, given that particular mean and standard deviation Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 481 The Standard Normal Distribution ? Also known as the “z” distribution ? Mean is defined to be 0 ? Standard Deviation is 1 z f(z) 0 1 Values above the mean have