{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(Statistics);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 52 "X := RandomVariable(Bernoulli(1/2)):\nDensityPlot(
X);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A := Sample(X, 10^6);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=n->add(A[i]-1/2,i=1..n);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plots[pointplot]([seq([n,f(n
)],n=1..2*10^3)],style=line);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "pl
ots[pointplot]([seq([n,A(n)-1/2],n=1..10^3)],style=line);\n\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 378 "g:=(n,k)->add(A[i]-1/2,i=n.
.min(n+k,10^6));\ng:=(n,k)->add(A[i]-1/2,i=k*n..min(n*(k+1)-1,10^6));
\ng:=(n,k)->add(A[i]-1/2,i=k*n..(n+1)*(k)-1);\n\nplots[pointplot]([seq
([n,g(n,1)],n=1..10^3)],style=line);\n\nplots[pointplot]([seq([n,g(n,1
0)],n=1..10^3)],style=line);\nplots[pointplot]([seq([n,g(n,75)],n=1..1
0^3)],style=line);\nplots[pointplot]([seq([n,g(n,200)],n=1..10^3)],sty
le=line);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "#Histogram(
[A]);\nHistogram([seq(g(n,1),n=1..1000)]);\nHistogram([seq(g(n,10),n=1
..1000)]);\nHistogram([seq(g(n,75),n=1..1000)]);\nHistogram([seq(g(n,2
00),n=1..1000)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "X := RandomVariable(Bernoull
i(1/2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "with(Statistics
):\ninfolevel[Statistics] := 1:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 72 "Calculate Shapiro and Wilk's W-test on the normally distributed
 sample. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "ShapiroWilkWTe
st([seq(g(n,1),n=1..4*100)], level=.05);\nShapiroWilkWTest([seq(g(n,10
),n=1..4*100)], level=.05);\nShapiroWilkWTest([seq(g(n,75),n=1..4*100)
], level=.05);\nShapiroWilkWTest([seq(g(n,200),n=1..4*100)], level=.05
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "X := RandomVariable(Nor
mal(0,1)):\nDensityPlot(X);\nPDF(X, u);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "A := Sample(X, 10^6);" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 23 "f:=n->add(A[i],i=1..n);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "
plots[pointplot]([seq([n,f(n)],n=1..10^3)],style=line);" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 55 "plots[pointplot]([seq([n,A(n)],n=1..10^4)],sty
le=line);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 61 "Z := RandomVariable(Pareto(1,2));\nDensityPlot
(Z);\nPDF(Z, u);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "A :=
 Sample(Z, 10^6)-Sample(Z, 10^6);\nHistogram(A);\nHistogram(A,range=-1
..1);\nHistogram(A,range=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "f:=n->add(A[i],i=1..n);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "plots[pointplot]([seq([n,f(n)],n=1..10^3)],style=line
);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots[pointplot]([seq([n,A(n)
],n=1..10^3)],style=line);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "plot(\{PDF(X,u),PDF(Z,u)\},u=1..20);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "plot(\{PDF(X,u),PDF(RandomVariable(Pareto(1,.25)),u)
\},u=0..20,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
43 "l:=(x,c)->sqrt(c/2/Pi)*exp(-c/2/x)/x^(3/2);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "limit(l(x,c),x=0,right);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 27 "solve(diff(l(x,c),x)=0,x);\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "c:='c';\nxx:=solve(diff(l(x,c),x)=0
,x);\nevalf(subs(x=xx,diff(l(x,c),x,x)));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 48 "int(l(x,c),x=0..infinity);\nint(l(x,c),x=0..1/6);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "L:=(x,c)->l((abs(x)+c/3)
,c)/int(l((abs(x)+c/3),c),x=-infinity..infinity);\n#solve(diff(L(x,c),
x)=0,x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot(\{L(x,1/2),L(x,1/3
),L(x,1),L(x,2)\},x=-1/2..1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 46 "simplify(int(L(x,3/2),x=-infinity..infinity));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "LL:=c-> Distribution(PDF=(x->L(x,c)
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "W:=RandomVariable(LL
(2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "DensityPlot(W);" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A := Sample(W, 10^6);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Mean(W);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "L :=c-> Distribution(PDF=(x
->piecewise(x<0,0,sqrt(c/2/Pi)*exp(-c/2/x)/x^(3/2))));\nc:=1/2;\n#L :=
 Distribution(PDF=(x->sqrt(c/2/Pi)*exp(-c/2/x)/x^(3/2)));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "L(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "U := Distribution(PDF = (t -> piecewise(t <= 0, 0, t \+
< 3, 1/3, 0)));;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "W:=Rand
omVariable(L(2));\nQ:=RandomVariable(U);\nPDF(W,u);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "plot(PDF(W,u),u=-5..5);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 15 "DensityPlot(W);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "A := Sample(W, 10^6);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 23 "f:=n->add(A[i],i=1..n);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "plots[pointplot]([seq([n,f(n)],n=1..10^3)],style=line
);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots[pointplot]([seq([n,A(n)
],n=1..10^3)],style=line);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(
\{PDF(X,u),PDF(Z,u)\},u=1..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 34 "A := Sample(Q, 10^6)-Sample(Z, 1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 23 "f:=n->add(A[i],i=1..n);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "plots[pointplot]([seq([n,f(n)],n=1..10^3)],style=line
);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots[pointplot]([seq([n,A(n)
],n=1..10^3)],style=line);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "#with(Statistics):\na:=1;b:=
2;\nX := RandomVariable(Cauchy(0,1/10)):\nPDF(X, u);\nDensityPlot(X);
\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"A := Sample(X, 10^6);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=n->add
(A[i],i=1..n);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots[pointplot](
[seq([n,f(n)],n=1..10^3)],style=line);" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 55 "plots[pointplot]([seq([n,A(n)],n=1..10^3)],style=line);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(
inttrans);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "eval(invfouri
er(exp(-2*abs(z)^(1/2)),z,x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 46 "xxx:=CharacteristicFunction('Normal'(0,1), z);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eval(invfourier(xxx,z,x));" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "64" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }