quiz1 - (b) Elicit a prior according to.expert's beliefs....

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ISyE8843 Brani Vidakovic Fliday, 8/27 /04 Name: 1. Lifetime. A lifetime X of a particular machine is modeled by an exponential distribution with unknown parameter 0. If theparametrizationis/(rl9) :0e-0', x)0,0 )0,theMLEestimatorfordis0unB:I/X onbasis of asample Xt,. ..,Xr. The lifetimes (in years) of X1 : 5, X2 :6, and Xs : 4 ate observed. (a) Write down the MLE of 0 for those observations. Assume now that an expert believes that d should have exponential distribution as well and that, on average d should be 1/3.
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Unformatted text preview: (b) Elicit a prior according to.expert's beliefs. (c) For the prior in (b), find tbe posterior. Is the problem conjugate? (d) Find the Bayes estimator Auoo.,, and compare it with the MLE estimator from (a). Discuss. Ca) (b) MLE, 0u. ..e :89 =TS r-(e) -3=1 o7o ='L-- j-x 5 -(") TrCelI )4!,^ry).7r(ol a<' e3et**, slo-+, tr(rg ) * fiorilm^- (+rbl. f , Tlre Droblem [s con iuaa+e Srnc-a +e\t Q+rone*rt 4s+rr'6u+r'tlJb a sf@ial a&< oG Qom,jlte (sha7e = I ) Ui t :* Ebf"s - 44==<-J t y u - . : ^ l t 8 7 /6o /sffi;rr^-#:2if ,* st^t*l:eA\ xre-l)o .e-,ci)7J[la"' :...
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