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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#\n# Varianz des Zen
tralwerts\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "#\n# Normalverteilung und F
ehlerfunktion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Phi:=z->1/
2+(1/2)*erf(z/sqrt(2));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "Phic:=z->(1/2)*erfc(z/sqrt(2));" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 31 "phi:=z->exp(-z*z/2)/sqrt(2*Pi);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "#\n# Normalverteilung\nF := x -> Ph
i(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "#\n# Logistische V
erteilung\n# F := x -> exp(x)/(1.0+exp(x));" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 87 "#\n# Cauchy-Verteilung\n# f := x -> 1/(Pi*(1+x^2))
;\n# F := x -> int(f(t),t=-infinity..x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "# F(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "
# int(x*f(x),x=0..infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "# plot(F(x),x=-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "# Laplaceverteilung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "
# f:=x->(1/2)*exp(-abs(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "# plot(f(x),x=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "# F := x -> int(f(t),t=-infinity..x);" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "# F(x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 71 "#\n# Rechtecksverteilung auf [-1,1]\n# f:=x->piecew
ise(x<-1,0,x>1,0,1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "# \+
f(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "# plot(f(x),x=-2..
2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# F := x -> int(f(t)
,t=-1..x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "# F(x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 279 "#\n# X1,...,Xn unabh\344ngi
g, je mit Vert.funktion F;\n# Y = Ze(X1,...,Xn) = Zentralwert von X1,.
..,Xn\n# G := Vert.funktion von Y\n# Erwartungswert von Y:\n#   E(Y) =
 int(y*g(y),y=-infinity..infinity) = mu\n# Varianz von Y:\n#   Var(Y) \+
= int((y-mu)^2*g(y),y=-infinity..infinity) = tau2 \n#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "#\n# Verteilung des Zentralwerts Y \+
= Ze(X1,...,Xn) = X(k+1) falls n=2k+1;\n# G := Vert.funktion von Y" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "G := y -> sum(binomial(n,j)
*F(y)^j*(1-F(y))^(n-j),j=k+1..n);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "g := y -> diff(G(y),y);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "g(y);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "k:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "n:=
2*k+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "# existiert der E
rw.wert?\nint(abs(y)*g(y),y=-infinity..infinity);\nevalf(%);" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "mu := int(y*g(y),
y=-infinity..infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "e
valf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "tau2 := int(y^2
*g(y),y=-infinity..infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "n*%;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(Pi/2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "37" 0 }{VIEWOPTS 1 1 0 
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