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Unformatted text preview: 8-2Solutions Manual for Statistical Inferenceandddylog(y) = log-log(1-)-logym-y1y+ logm-ym+ (m-y)1m-y= logy/m(m-ym)1-!.Fory/m > , 1-y/m= (m-y)/m <1-, so each fraction above is less than 1, and thelog is less than 0. Thusddylog <0 which shows thatis decreasing inyand(y)< cif andonly ify > b.8.4 For discrete random variables,L(|x) =f(x|) =P(X=x|). So the numerator and denomi-nator of(x) are the supremum of this probability over the indicated sets.8.5 a. The log-likelihood islogL(,|x) =nlog+nlog-(+ 1)logYixi!,x(1),wherex(1)= minixi. For any value of, this is an increasing function offorx(1). Soboth the restricted and unrestricted MLEs ofare =x(1). To find the MLE of, setlogL(,x(1)|x) =n+nlogx(1)-logYixi!= 0,and solve foryielding=nlog(Qixi/xn(1))=nT.(2/2)logL(,x(1)|x) =-n/2<0, for all. Sois a maximum....
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This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.
- Spring '12