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)