商务与经济统计习题答案（第8版，中文版）SBE8-SM05

5-1Chapter5DiscreteProbabilityDistributionsLearningObjectives1.Understandtheconceptsofarandomvariableandaprobabilitydistribution.2.Beabletodistinguishbetweendiscreteandcontinuousrandomvariables.3.Beabletocomputeandinterprettheexpectedvalue,variance,andstandarddeviationforadiscreterandomvariable.4.Beabletocomputeandworkwithprobabilitiesinvolvingabinomialprobabilitydistribution.5.BeabletocomputeandworkwithprobabilitiesinvolvingaPoissonprobabilitydistribution.6.Knowwhenandhowtousethehypergeometricprobabilitydistribution.Chapter55-2Solutions:1.a.Head,Head(H,H)Head,Tail(H,T)Tail,Head(T,H)Tail,Tail(T,T)b.x=numberofheadsontwocointossesc.OutcomeValuesofx(H,H)2(H,T)1(T,H)1(T,T)0d.Discrete.Itmayassume3values:0,1,and2.2.a.Letx=time(inminutes)toassembletheproduct.b.Itmayassumeanypositivevalue:x0.c.Continuous3.LetY=positionisofferedN=positionisnotoffereda.S={(Y,Y,Y),(Y,Y,N),(Y,N,Y),(Y,N,N),(N,Y,Y),(N,Y,N),(N,N,Y),(N,N,N)}b.LetN=numberofoffersmade;Nisadiscreterandomvariable.c.ExperimentalOutcome(Y,Y,Y)(Y,Y,N)(Y,N,Y)(Y,N,N)(N,Y,Y)(N,Y,N)(N,N,Y)(N,N,N)ValueofN322121104.x=0,1,2,...,12.5.a.S={(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)}b.ExperimentalOutcome(1,1)(1,2)(1,3)(2,1)(2,2)(2,3)NumberofStepsRequired2343456.a.values:0,1,2,...,20discreteb.values:0,1,2,...discretec.values:0,1,2,...,50discreteDiscreteProbabilityDistributions5-3d.values:0x8continuouse.values:x0continuous7.a.f(x)0forallvaluesofx.f(x)=1Therefore,itisaproperprobabilitydistribution.b.Probabilityx=30isf(30)=.25c.Probabilityx25isf(20)+f(25)=.20+.15=.35d.Probabilityx30isf(35)=.408.a.xf(x)13/20=.1525/20=.2538/20=.4044/20=.20Total1.00b.c.f(x)0forx=1,2,3,4.f(x)=19.a.xf(x)115/462=0.032232/462=0.069384/462=0.1824300/462=0.650531/462=0.067Chapter55-4b.0.150.300.450.60f(x)x123405c.Allf(x)0f(x)=0.032+0.069+0.182+0.650+0.067=1.00010.a.xf(x)10.0520.0930.0340.4250.411.00b.xf(x)10.0420.1030.1240.4650.281.00c.P(4or5)=f(4)+f(5)=0.42+0.41=0.83d.Probabilityofverysatisfied:0.28e.Seniorexecutivesappeartobemoresatisfiedthanmiddlemanagers.83%ofseniorexecutiveshaveascoreof4or5with41%reportinga5.Only28%ofmiddlemanagersreportbeingverysatisfied.11.a.DiscreteProbabilityDistributions5-5DurationofCallxf(x)10.2520.2530.2540.251.00b.0.100.200.30f(x)x12340c.f(x)0andf(1)+f(2)+f(3)+f(4)=0.25+0.25+0.25+0.25=1.00d.f(3)=0.25e.P(overtime)=f(3)+f(4)=0.25+0.25=0.5012.a.Yes;f(x)0forallxandf(x)=.15+.20+.30+.25+.10=1b.P(1200orless)=f(1000)+f(1100)+f(1200)=.15+.20+.30=.6513.a.Yes,sincef(x)0forx=1,2,3andf(x)=f(1)+f(2)+f(3)=1/6+2/6+3/6=1b.f(2)=2/6=.333c.f(2)+f(3)=2/6+3/6=.83314.a.f(200)=1-f(-100)-f(0)-f(50)-f(100)-f(150)=1-.95=.05ThisistheprobabilityMRAwillhavea$200,000profit.b.P(Profit)=f(50)+f(100)+f(150)+f(200)=.30+.25+.10+.05=.70c.P(atleast100)=f(100)+f(150)+f(200)=.25+.10+.05=.4015.a.xf(x)xf(x)3.25.75Chapter55-66.503.009.252.251.006.00E(x)==6.00b.xx-(x-)2f(x)(x-)2f(x)3-39.252.25600.500.00939.252.254.50Var(x)=2=4.50c.=4.50=2.1216.a.yf(y)yf(y)2.20.404.301.207.402.808.10.801.005.20E(y)==5.20b.yy-(y-)2f(y)(y-)2f(y)2-3.2010.24.202.0484-1.201.44.30.43271.803.24.401.29682.807.84.10.7844.560Var()...y45645621417.a/b.xf(x)xf(x)x-(x-)2(x-)2f(x)0.10.00-2.456.0025.6002501.15.15-1.452.1025.3153752.30.60-.45.2025.0607503.20.60.55.3025.0605004.15.601.552.4025.3603755.10.502.556.5025.6502502.452.047500E(x)==2.452=2.0475=1.430918.a/b.DiscreteProbabilityDistributions5-7xf(x)xf(x)x-(x-)2(x-)2f(x)0.010-2.35.290.05291.23.23-1.31.690.38872.41.82-0.30.090.03693.20.600.70.490.0984.10.401.72.890.2895.05.252.77.290.36452.31.23E(x)=2.3Var(x)=1.231.231.11Theexpectedvalue,E(x)=2.3,oftheprobabilitydistributionisthesameasthatreportedinthe1997StatisticalAbstractoftheUnitedStates.19.a.E(x)=xf(x)=0(.50)+2(.50)=1.00b.E(x)=xf(x)=0(.61)+3(.39)=1.17c.Theexpectedvalueofa3-pointshotishigher.So,iftheseprobabilitiesholdup,theteamwillmakemorepointsinthelongrunwiththe3-pointshot.20.a.xf(x)xf(x)0.900.00400.0416.001000.0330.002000.0120.004000.0140.006000.0160.001.00166.00E(x)=166.Ifthecompanychargedapremiumof$166.00theywouldbreakeven.b.GaintoPolicyHolderf(Gain)(Gain)f(Gain)-260.00.90-234.00140.00.045.60740.00.0322.201,740.00.0117.403,740.00.0137.405,740.00.0157.40-94.00E(gain)=-94.00.Thepolicyholderismoreconcernedthatthebigaccidentwillbreakhimthanwiththeexpectedannuallossof$94.00.21.a.E(x)=xf(x)=0.05(1)+0.09(2)+0.03(3)+0.42(4)+0.41(5)=4.05b.E(x)=xf(x)=0.04(1)+0.10(2)+0.12(3)+0.46(4)+0.28(5)=3.84c.Executives:2=(x-)2f(x)=1.2475Chapter55-8MiddleManagers:2=(x-)2f(x)=1.1344d.Executives:=1.1169MiddleManagers:=1.0651e.Theseniorexecutiveshaveahigheraveragescore:4.05vs.3.84forthemiddlemanagers.Theexecutivesalsohaveaslightlyhigherstandarddeviation.22.a.E(x)=xf(x)=300(.20)+400(.30)+500(.35)+600(.15)=445Themonthlyorderquantityshouldbe445units.b.Cost:445@$50=$22,250Revenue:300@$70=21,000$1,250Loss23.a.Laptop:E(x)=.47(0)+.45(1)+.06(2)+.02(3)=.63Desktop:E(x)=.06(0)+.56(1)+.28(2)+.10(3)=1.42b.Laptop:Var(x)=.47(-.63)2+.45(.37)2+.06(1.37)2+.02(2.37)2=.4731Desktop:Var(x)=.06(-1.42)2+.56(-.42)2+.28(.58)2+.10(1.58)2=.5