资源描述：
《chapter1习题答案》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Chapter１習題答案1.7ProveBonferroni’sinequality:P(AB)P(A)+P(B)–1SOL:P(AB)=P(A)+P(B)–P(AB)1P(AB)P(A)+P(B)–11.8ProvethatP()SOL:provethatP()n=2P()=P(AA)=P(A)+P(A)-P(AA)設n=k成立即P()n=k+1時P()=P(()A)P()+P(A)[]+P(A)=由數學歸納法得知P()1.9TheweatherforecastersaysthattheprobabilityofrainonSat
2、urdayis25%andthattheprobabilityofrainonSundayis25%.Istheprobabilityofrainduringtheweekend50%?Whyorwhynot?SOL:No,theprobabilityofrainduringtheweekendis１–1.34Provethefollowingidentity:=SOL:letΧbeahypergeometricrandomvariableP(X=x
3、N,M,K)=x=0、1、2k=letN=m,M=n,k=nwehave=即=1.
4、59Aboxhasthreecoins.Onehastwoheads,onehastwotails,andtheotherisafaircoinwithoneheadandonetail.Acoinischosenatrandom,siflipped,andcomesupheads.a.Whatistheprobabilitythatthecoinchosenisthetwo-headedcoin?b.Whatistheprobabilitythatifisisthrownanothertimeitwillcomeupheads?c
5、.Answerpart(a)again,supposingthatthecoinisthrowasecondtimeandcomesupheadsagain.©.SOL:A:twoheadedcoinB:oneheadandonetailcoinC:twotailedcoinP(A
6、headandhead)====1.62ShowthatifP(A
7、E)P(B
8、E)andP(A
9、E)P(B
10、E),thenP(A)P(B).SOL:P(A
11、E)P(B
12、E)P(AE)P(BE)P(A
13、E)P(B
14、E)P(AE)P(BE)P(AE)+P(
15、AE)P(BE)+P(BE)P(A)P(B)1.69IfAandBaredisjoint,cantheybeindependent?SOL:IFA,B(P(A)>0,P(B)>0)IFAandBaredisjoint,thenAandBmustbedependent.IFsupposeAandBareindependent,0=P(AB)=P(A)P(B)01.79Manyhumandiseasesaregeneticallytransmitted(forexample,hemophiliaorTay-Sachsdisease).H
16、ereisasimplemodelforsuchadisease.Thegenotypeaaisdiseasedanddiesbeforeitmates.ThegenotypeAaisacarrierbutisnotdiseased.ThegenotypeAAisnotacarrierandisnotdiseased.a.Iftwocarriersmate,whataretheprobabilitiesthattheiroffspringareofeachofthethreegenotypes?b.Ifthemaleoffsprin
17、goftwocarriersisnotdiseased,whatistheprobabilitythatheisacarrier?c.Supposethatthenondiseasedoffspringofpart(b)mateswithamemberofthepopulationforwhomnofamilyhistoryisavailableandwhoisthusassumedtohaveprobabilitypofbeingacarrier(pisaverysmallnumber).Whataretheprobabiliti
18、esthattheirfirstoffspringhasthegenotypesAA,Aa,andaa?d.Supposethatthefirstoffspringofpart©isnotdiseased.Whatistheproba
