Elliot Tanis
February 13, 2006
Exercise 5.4-2 (Exercise_5_4-2.mws)

 > XX := [12.0, 9.4, 10.0, 13.5, 9.3, 10.1, 9.6, 9.3, 9.1, 9.2, 11.0, 9.1, 10.4, 9.1, 13.3, 10.6]:

 > Probs := [seq(1/16, k = 1 .. 16)]: XXPDF := zip((XX,Probs)-> (XX,Probs), XX, Probs);

 > for k from 1 to 200 do   X := DiscreteS(XXPDF, 16):   Svar[k] := Variance(X): od: Svars := [seq(Svar[k], k = 1 .. 200)]:

 > Mean(Svars);

 > xtics := [seq(0.4*k, k = 1 .. 12)]: ytics := [seq(0.05*k, k = 1 .. 13)]: P1 := plot([[0,0],[0,0]], x = 0 .. 4.45, y = 0 .. 0.61, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]): P2 := HistogramFill(Svars,0 .. 4.4, 11): display({P1, P2});

Histogram of 200   using resamples of size n  = 16

Exercise 5.4-2(b)

 > theta := Mean(XX) - 9; for k from 1 to 200 do   Y := ExponentialS(theta,16):   Svary[k] := Variance(Y): od: Svarys := [seq(Svary[k], k = 1 .. 200)]:

 > Mean(Svarys); Max(Svarys);

 > xtics := [seq(0.8*k, k = 1 .. 14)]: ytics := [seq(0.05*k, k = 1 .. 16)]: P3 := plot([[0,0],[0,0]], x = 0 .. 8.07, y = 0 .. 0.49, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]): P4 := HistogramFill(Svarys,0 .. 8.0, 20): display({P3, P4});

Exercise 5.4-2(c)

 > Svars := sort(Svars): Svarys := sort(Svarys):

 > xtics := [seq(k*0.5, k = 1 .. 18)]: ytics := [seq(k*0.5, k = 1 .. 18)]: P5 := plot([[0,0],[0,0]], x = 0 .. 5, y = 0 .. 9, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]): P6 := ScatPlotCirc(Svars,Svarys): display({P5, P6});

What is your conclusion and why?