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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#Pitman-Sch\344tzer \+
(vgl. Aufgabe 21)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# Dreiecksverteilung a
uf [-1,+1]\n# f:=x->piecewise(x<0,x+1,x>0,1-x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 46 "# Rechtecksverteilung auf [-1,+1]\n# f:=x->1/2
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "# Normalverteilung N(0
,1)\n# f:=x->1/(sqrt(2*Pi))*exp(-x^2/2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "# Cauchyverteilung C(0,1)\n f:=x->1/(Pi*(1+x^2));" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=-2..2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x1:=1.0;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "x2:=1.8;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "x3:=2.1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
x4:=1.9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x5:=2.7;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "# m:=min(x1,x2,x3,x4,x5);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "# M:=max(x1,x2,x3,x4,x5);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "#Zaehler:=int(z*f(x1-z
)*f(x2-z)*f(x3-z)*f(x4-z)*f(x5-z),z=M-1..m+1);\nZaehler:=int(z*f(x1-z)
*f(x2-z)*f(x3-z)*f(x4-z)*f(x5-z),z=-infinity..+infinity);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "#Nenner:=int(f(x1-z)*f(x2-z)*f(x3-
z)*f(x4-z)*f(x5-z),z=M-1..m+1);\nNenner:=int(f(x1-z)*f(x2-z)*f(x3-z)*f
(x4-z)*f(x5-z),z=-infinity..+infinity);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "# Pitman-Sch\344tzer:\ntheta_dach:=Zaehler/Nenner;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "# ML-Sch\344tzer:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "#Likelihood-Funktion\nL:=the
ta->f(x1-theta)*f(x2-theta)*f(x3-theta)*f(x4-theta)*f(x5-theta);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "#plot(L(theta),theta=M-1..m+
1);\nplot(L(theta),theta=0..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "L_strich:=diff(L(theta),theta);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "#plot(L_strich,theta=M-1..m+1);\nplot(L_strich,theta=
1..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "# ML-Sch\344tzer:
\nfsolve(L_strich=0,theta=1..3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "5 0 0" 18 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }