Dr. Hackney STA Solutions pg 41

Dr. Hackney STA Solutions pg 41 - 3-14Solutions Manual for...

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Unformatted text preview: 3-14Solutions Manual for Statistical InferenceThe inequality is becausex-2> x-1, andFis nondecreasing. To get strict inequalityfor somex, let (a,b] be an interval of length1-2withP(a < Zb) =F(b)-F(a)>0.Letx=a+1. ThenF(x|1)=F(x-1) =F(a+1-1) =F(a)< F(b) =F(a+1-2) =F(x-2) =F(x|2).b. Let1> 2. LetX1f(x/1) andX2f(x/2). LetF(z) be the cdf corresponding tof(z) and letZf(z). Then, forx >0,F(x|1)=P(X1x) =P(1Zx) =P(Zx/1) =F(x/1)F(x/2) =P(Zx/2) =P(2Zx) =P(X2x)=F(x|2).The inequality is becausex/2> x/1(becausex >0 and1> 2>0), andFisnondecreasing. Forx0,F(x|1) =P(X1x) = 0 =P(X2x) =F(x|2). Toget strict inequality for somex, let (a,b] be an interval such thata >0,b/a=1/2andP(a < Zb) =F(b)-F(a)>0. Letx=a1. ThenF(x|1)=F(x/1) =F(a1/1) =F(a)< F(b) =F(a1/2) =F(x/2)=F(x|2).3.43 a.FY(y|) = 1-FX(1y|)y >0, by Theorem 2.1.3. For1> 2,FY(y|1) = 1-FX1y11-FX1y2=FY(y|2)for all...
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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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