CHAPTER 5 Discrete Probability DistributionStat 200 – Elementary StatisticsIntroductionSection 5.1 Probability DistributionDiscrete Probability DistributionWrite the distribution for the formulaSection 5.2 Mean, Variance, Standard Deviation and ExpectationSection 5.3 Binomial DistributionStat 200 – Elementary Statistics IntroductionThis chapter explains the concepts and applications of probability distributions. In addition, special probability distributions, such as the binomial, multinomial, Poisson, and hypergeometric distributions are explainedSection 5.1 Probability DistributionRandom variableExampleConstruct a probability distribution for flipping three coins.Discrete Probability DistributionExampleConstruct a probability distribution for rolling a single die.Graphing the probabilityN. of heads 0 1 2 3ProbabilityTwo Requirements for a Probability Distribution1.2.Student NotesCHAPTER 5 Discrete Probability DistributionExampleWrite the distribution for the formula P(X) = 1/X, where X = 2, 3, 6Section 5.2 Mean, Variance, Standard Deviation and ExpectationCalculating MeanExamples1. Find the mean of the number of spots that appear when a die is tossed.2. In a family with two children, find the mean of the number of children who will be girls.3. If three coins are tossed, find the mean of the number of heads that occur.Variance of a Probability DistributionExamples2 2 2[ ( )]X P Xs m= � -�2Compute the variance and standard deviation of the number of spots that appear when a die is tossed.Five balls numbers 0, 2, 4, 6, and 8 are placed in a bag. After the balls are mixed, one is selected, its number is noted, and then it is replaced. If this experiment is repeated many times, find the variance and standard deviation of the numbers on the balls.Expected ValueExampleOne thousand tickets are sold at $1 each for a color television valued at $350. What is the expected value of the gain if a person purchases one ticket?Section 5.3 Binomial DistributionThe binomial experiment is a probability experiment that satisfies these requirements:1. Each trial can have only two possible outcomes—_____________ or ______________.2. There must be a __________ number of trials.3. The outcomes of each trial must be ______________________ of each other.4. The probability of success must remain the ______________ for each trial.Notation for the Binomial DistributionBinomial Probability FormulaExamplesA coin is tossed three times. Find the probability of getting exactly two heads.A survey found that one out of five Americans say he or she has visited a doctor in any given month. If 10 people are selected at random, find the probability that exactly 3 will have visited a doctor last month.A coin is tossed three times. Find the probability of getting exactly two heads using table B (p 756).Binomial Distribution PropertiesMeanVarianceStandard DeviationA coin is tossed 4 times. Find the mean, variance, and standard deviation of the number of headsthat will be obtained.A die is rolled 480 times. Find the mean, variance, and standard deviation of the number of 2s that will be rolled.!( )( )! !X n XnP X p qn X X-= �
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