3342 Review: Chapters 4 - 7.2Terms and Representative ProblemsChapter 4random variable probability distribution 2-5f (x) $ 0()1allxfx=∑discrete random variablecontinuous random variableprobability histogramcumulative distribution functionbinomial distribution 13-20two outcomes per trialp(success) same for all trialsfixed number, n, of trialstrials are independentbinomial distribution functionb(x;n,p) 7cumulative binomial distribution functionB(x;n,p)symmetricpositively skewednegatively skewedhypergeometric distribution 22-27sampling without replacementhypergeometric distribution functionh(x;n,a,N)mean 30, 32binomial 38-39hypergeometricvariance and standard deviation 30, 32binomial hypergeometrickth moment about the originalternate formula for variance 31, 33Chebyschev's Theorem 44-45law of large numbersPoisson distribution 54-57mean and varianceapproximation to binomial 52-53Poisson process 63-65geometric distribution 60, 62mean and variancemultinomial distribution 70, 72mean and varianceChapter 5probability density function 2, 4, 6, 9-10, 108f (x) $ 0()1fxdx∞−∞=∫distribution function 5kth moment about the originmean, variance and standard deviation 13-14normal distribution 24, 27, 29, 31, 33mean and variancestandard normal distribution 19-21, 112-113Table 3standardized random variableXZµσ−=normal approximation to binomial 35-39continuity correctionuniform distribution 46, 110log-normal distribution 50-51, 55, 115gamma distribution 54gamma functionfunctional equation (1)()xxxΓ+=Γexponential distribution 58-60, 117waiting time between successive arrivalsbeta distribution 64-65Weibull distribution 68-69, 121Chapter 6populationfiniteinfinitesamplerandom samplefinite populationinfinite populationpopulation parameterssample statisticssampling distributionTheorem 6.1 Mean and variance of a samplingdistributionxµµ=2221xnNnnNσσσ=−−finite population correction factorstandard error of the mean/xnσσ=standardized sampling mean 15-17/xZnµσ−=Theorem 6.2 Central Limit Theorema) normal distribution approximation for samplingdistribution of the mean for 25n≥b) sampling distribution of the mean is normal ifpopulation normalt-distribution 20-24degrees of freedomTable 4standard normal distribution approximation for t-distribution for 30n ≥sampling distribution of the variancechi-square distribution 27Table 5F-distribution Table 6left-hand probability 26112211(,)(,)FFαανννν−=Chapter 7point estimationparameterestimatorestimate of standard errorunbiased estimatormore efficient unbiased estimatormaximum error of estimate 6, 8-12/2Eznασ=confidenceinterval estimate confidence interval 15, 17-21/2/2xzxznnαασσµ−<<+degree of confidenceconfidence