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英文的统计学高数,超急QUESTION4(a)Astudentanswersamultiple-choiceexaminationquestionwhichoffersfourpossibleanswers.Supposethattheprobabilitythatthestudentknowstheanswertothequestionis0.8andtheprobabilitythathe/s
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问题描述:

英文的统计学高数,超急

QUESTION4

(a)Astudentanswersamultiple-choiceexaminationquestionwhichoffersfourpossibleanswers.Supposethattheprobabilitythatthestudentknowstheanswertothequestionis0.8andtheprobabilitythathe/shewillguessis0.2.Assumethat,ifthestudentguesses,theprobabilityofguessingcorrectlyis0.25.Ifthestudentcorrectlyanswersthequestion,whatistheprobabilitythathe/shedidsobyguessing?(Hint:usingBayes’Theorem)

(6marks)

(b)Inanexperiment,ifamouseisadministereddosagelevelAofacertain(harmless)hormonethenthereisa0.2probabilitythatthemousewillshowsignsofaggressionwithinoneminute.FordosagelevelsBandC,theprobabilitiesare0.5and0.8,respectively.Tenmicearegivenexactlythesamedosagelevelofthehormoneand,ofthese,exactly6showssignsofaggressionwithinoneminuteofreceivingthedose.

i)CalculatetheprobabilityofthishappeningforthedosagelevelA.(ThisisessentiallyaBinomialrandomvariableproblem)

(6marks)

ii)Assumingthateachofthethreedosagelevelswasequallylikelytohavebeenadministeredinthefirstplace(withaprobabilityof1/3),useBayes’TheoremtoevaluatethelikelihoodofthedosagelevelAgiventhat6outofthe10micewereobservedtoreactinthisway.

(8marks)

Total(20marks)

骆斌回答:
  先说清贝叶斯法则P(A交B)=P(B|A)*P(A)=P(A|B)*P(B)   soP(A|B)=P(B|A)*P(A)/P(B)   Q4(a)问的是P(guessIcorrect)   P(correctIguess)=0.25   P(guess)=0.2   P(notguess)=0.8   P(correctInotguess)=1   0.2*0.25/(0.2*0.25+0.8*1)=0.0588   b)1)二项式分布binomialdistribution:C(10,6)*0.2^6*0.8^4=0.005505024   2)问P(dosageAI6positive)   已知   P(dosageA)=1/3   P(dosageB)=1/3   P(dosageC)=1/3   P(6positiveIdosageA)=0.005505024   同样可计算   P(6positiveIdosageB)=C(10,6)*0.5^6*0.5^4=0.205078125   P(6positiveIdosageC)=C(10,6)*0.8^6*0.2^4=0.088080384   答案=(0.005505024*1/3)/(0.005505024*1/3+0.205078125*1/3+0.088080384*1/3)   =0.018432
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