>    restart:
read `C:\\Tanis-Hogg\\Maple Examples\\stat.m`:

Elliot Tanis
April 20, 2006
Exercise 5.3-4 (Exercise_5_3-4.mws)

Exercise 5.3-4

>    f := 2*x;

f := 2*x

>    mu := int(x*f, x = 0 .. 1);
evalf(%);

mu := 2/3

.6666666667

>    var := int((x - mu)^2*f, x = 0 .. 1);
evalf(%);
sigma := evalf(sqrt(var));

var := 1/18

.5555555556e-1

sigma := .2357022604

>    for j from 1 to 1000 do
  for k from 1 to 18 do
    XX[k] := evalf(sqrt(rng())):
  od:
  X := [seq(XX[k], k = 1 .. 18)]:
  Xbar[j] := Mean(X):
od:
Xbars := [seq(Xbar[j], j = 1 .. 1000)]:

>    Mean(Xbars);

.6639037758

>    Variance(Xbars);

.3085498498e-2

>    evalf(var/18);

.3086419753e-2

>    Min(Xbars), Max(Xbars);

.5037304720, .8434598228

Now construct a histogram with a N (2/3, (1/18)/18) p.d.f. superimposed.

>    xtics := [seq(0.4 + k*0.05, k = 0 .. 10)]:
ytics := [seq(0.5*k, k = 1 .. 15)]:
P1 := plot(NormalPDF(mu, var/18, x), x = 0.4 .. 0.9,y = 0 .. 7.7, color=black, thickness=2, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]):
P2 := HistogramFill(Xbars, 0.40 .. 0.90, 20):
display({P1, P2});

[Maple Plot]

>   

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