3342 Review: Chapters 4 - 6Terms and Representative ProblemsChapter 4random variable probability distribution 2-5f (x) 0≥() 1all xfx=∑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 23-28sampling without replacementhypergeometric distribution functionh(x;n,a,N)mean 32, 34binomial 38-39hypergeometricvariance and standard deviation 32, 34binomial hypergeometrickth moment about the originalternate formula for variance 33, 35Chebyschev's Theorem 46-47law of large numbersPoisson distribution 56-59mean and varianceapproximation to binomial 54-55Poisson process 65-66geometric distribution 62, 64mean 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 64-65Chapter 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 forsampling distribution of the mean for 25n ≥b) sampling distribution of the mean is normal ifpopulation normalt-distribution 20-24degrees of freedomTable 4standard normal distribution approximation fort-distribution for 30n ≥sampling distribution of the variancechi-square distribution 27Table 5F-distribution Table 6left-hand probability 26112211(,