Dr. Hackney STA Solutions pg 127

Dr. Hackney STA Solutions pg 127 - 8-6Solutions Manual for...

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Unformatted text preview: 8-6Solutions Manual for Statistical InferenceThis is a quadratic inwith solution for the MLER= x+qx+4(2+x2)2.which yields the LRT statistic(x) =L(R|x)L(a,|x)=Qni=11p22Re-(xi-R)2/(22R)Qni=112a2e-(xi-)2/(2a2)=Rne(n/2)-i(xi-R)2/(2R).8.9 a. The MLE ofunderHis=(Y)-1, and the MLE ofiunderH1isi=Y-1i. TheLRT statistic is bounded above by 1 and is given by1(Y)-ne-n(QiYi)-1e-n.Rearrangement of this inequality yieldsY(QiYi)1/n, the arithmetic-geometric meaninequality.b. The pdf ofXiisf(xi|i) = (i/x2i)e-i/xi,xi>0. The MLE ofunderHis=n/[i(1/Xi)], and the MLE ofiunderH1isi=Xi. Now, the argument proceeds as inpart (a).8.10 LetY=iXi. The posterior distribution of|yis gamma(y+,/(+ 1)).a.P(|y) =(+1)y+(y+)y+Zty+-1e-t(+1)/dt.P( > |y) = 1-P(|y)....
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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.

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