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

Exercise 5.4-2(a)

>    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);

XXPDF := [12.0, 1/16, 9.4, 1/16, 10.0, 1/16, 13.5, 1/16, 9.3, 1/16, 10.1, 1/16, 9.6, 1/16, 9.3, 1/16, 9.1, 1/16, 9.2, 1/16, 11.0, 1/16, 9.1, 1/16, 10.4, 1/16, 9.1, 1/16, 13.3, 1/16, 10.6, 1/16]
XXPDF := [12.0, 1/16, 9.4, 1/16, 10.0, 1/16, 13.5, 1/16, 9.3, 1/16, 10.1, 1/16, 9.6, 1/16, 9.3, 1/16, 9.1, 1/16, 9.2, 1/16, 11.0, 1/16, 9.1, 1/16, 10.4, 1/16, 9.1, 1/16, 13.3, 1/16, 10.6, 1/16]

>    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);

1.922281873

>    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});

[Maple Plot]

Histogram of 200 S^2   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)]:

theta := 1.31250000

>    Mean(Svarys);
Max(Svarys);

1.682318804

8.579667233

>    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});

`WARNING: There are`, 1, ` data points out of plot range.`

[Maple Plot]

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});

[Maple Plot]

What is your conclusion and why?

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