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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 [email protected] €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"' :...
View Full Document

This note was uploaded on 10/23/2011 for the course ISYE 8843 taught by Professor Vidakovic during the Spring '11 term at Georgia Tech.

Ask a homework question - tutors are online