# binf, binF: Binomialverteilung # Z\344hldichte b(n,p;k), V-Funktion F(n,p;k)binf := proc(n,p,k) return evalf( binomial(n,k)*p^k*(1-p)^(n-k) ); end proc:binF := proc(n,p,k) local i; return evalf( sum(binf(n,p,i),i=0..k) ); end proc:# hypf, hypF: Hypergeometrische Verteilung # Z\344hldichte h(N,K,n;k), V-Funktion F(N,K,n;k)hypf := proc(N,K,n,k) return evalf( binomial(K,k)*binomial(N-K,n-k)/binomial(N,n) ); end proc:hypF := proc(N,K,n,k) local i; return evalf( sum(hypf(N,K,n,i),i=0..k) ); end proc:# poif, poiF: Poisson-Verteilung # Z\344hldichte pi(lambda;k), V-Funktion F(lambda;k)poif := proc(la,k) return evalf( exp(-la)*la^k/k! ); end proc:poiF := proc(la,k) local i; return evalf( sum(poif(la,i),i=0..k) ); end proc:# norf, norF: Normalverteilung # Dichtefunktion f(a,sig;x), v-Funktion F(a,sig;x)norf := (a,sig,x) -> evalf(1/(sig*sqrt(2*Pi)))*exp((-1/2)*((x-a)/sig)^2):norF := (a,sig,x) -> evalf( int(norf(a,sig,t),t=-infinity..x)):# chif, chiF: Chi-Quadrat-Verteilung # Dichtefunktion f(z,n), v-Funktion F(z,n)chif := proc(z,n) local an; an:=(n)->1/(2^(n/2)*GAMMA(n/2)); return evalf(an(n)*z^((n-2)/2)*exp(-z/2)); end proc:chiF := proc(z,n) local an; an:=(n)->1/(2^(n/2)*GAMMA(n/2)); return evalf(an(n)*int(u^((n-2)/2)*exp(-u/2),u=0..z)); end proc:# tf, tF: t-Verteilung # Dichtefunktion f(t,n), v-Funktion F(t,n)tf := proc(t,n) local an; an:=(n)->GAMMA((n+1)/2)/(sqrt(Pi*n)*GAMMA(n/2)); return evalf(an(n)*1/(1+t^2/n)^((n+1)/2)); end proc:tF := proc(t,n) return evalf(int(tf(v,n),v=-infinity..t));end proc:mittelwert := proc(l) return sum(l[i],i=1..nops(l))/nops(l); end proc:varStich := proc(l) local m; m := mittelwert(l); return 1/nops(l)*sum((l[i]-m)^2,i=1..nops(l)); end proc:varGesamt := proc(l) local m; m := mittelwert(l); return 1/(nops(l)-1)*sum((l[i]-m)^2,i=1..nops(l)); end proc:

restart;l:=[10.3,14.2,11.8,7.7,8.9,15.1,6.4,8.2,10.5,7.4,9.2,9.9,14.1,13.8,6.9];

NiM+SSJsRzYiNzEkIiQuIiEiIiQiJFUiRikkIiQ9IkYpJCIjeEYpJCIjKilGKSQiJF4iRikkIiNrRikkIiMjKUYpJCIkMCJGKSQiI3VGKSQiIyMqRikkIiMqKkYpJCIkVCJGKSQiJFEiRikkIiNwRik=

n:=nops(l);

NiM+SSJuRzYiIiM6

xm:=mittelwert(l);

NiM+SSN4bUc2IiQiK0xMTEg1ISIp

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.986;

NiM+SSNnYUc2IiQiJCcpKiEiJA==

# Varianz der Grundgesamtheits2:=1/(n-1)*sum((l[i]-xm)^2,i=1..n);

NiM+SSNzMkc2IiQiK2ttbV0kKSEiKg==

s:=sqrt(s2);

NiM+SSJzRzYiJCIrMj92KilHISIq

c:=fsolve(2*tF(x,n-1)-1=ga,x);

NiM+SSJjRzYiJCIrJVIsbCFHISIq

muMin:=evalf(xm-((c*s)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiKzdqSio+KSEiKg==

muMin:=evalf(xm+((c*s)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiK05ddFE3ISIp

xm:=mittelwert(l);

NiM+SSN4bUc2IiQiK0xMTEg1ISIp

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.982;

NiM+SSNnYUc2IiQiJCMpKiEiJA==

s2:=1/(n-1)*sum((l[i]-xm)^2,i=1..n);

NiM+SSNzMkc2IiQiK2ttbV0kKSEiKg==

c1:=fsolve(chiF(x,n-1)=(1-ga)/2,x);

NiM+SSNjMUc2IiQiKzltUGtYISIq

c2:=fsolve(chiF(x,n-1)=(1+ga)/2,x);

NiM+SSNjMkc2IiQiK2UqZXglSCEiKQ==

minSig2:=((n-1)*s2)/c2;

NiM+SShtaW5TaWcyRzYiJCIrXjYvbVIhIio=

maxSig2:=((n-1)*s2)/c1;

NiM+SShtYXhTaWcyRzYiJCIrTUdNaEQhIik=

minSig:=sqrt(minSig2);

NiM+SSdtaW5TaWdHNiIkIisjPiNcIio+ISIq

maxSig:=sqrt(maxSig2);

NiM+SSdtYXhTaWdHNiIkIisoM3I0MSYhIio=

restart;serverF:=(t,alpha,s)->1-alpha*s*exp(-alpha*t);

NiM+SShzZXJ2ZXJGRzYiZio2JUkidEdGJUkmYWxwaGFHRiVJInNHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmIiIiRi8qKDklRi85JkYvLUkkZXhwR0YlNiMsJComRjFGLzkkRi8hIiJGL0Y5RiVGJUYl

serverf:=unapply(diff(serverF(t,alpha,s),t),t,alpha,s);

NiM+SShzZXJ2ZXJmRzYiZio2JUkidEdGJUkmYWxwaGFHRiVJInNHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooOSUiIiM5JiIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y2SShfc3lzbGliR0YlNiMsJComRi9GMjkkRjIhIiJGMkYlRiVGJQ==

serverf:=(t,alpha,s)->alpha^2*s*exp(-alpha*t);

NiM+SShzZXJ2ZXJmRzYiZio2JUkidEdGJUkmYWxwaGFHRiVJInNHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooOSUiIiM5JiIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y2SShfc3lzbGliR0YlNiMsJComRi9GMjkkRjIhIiJGMkYlRiVGJQ==

test:=int(serverf(t,alpha,s),t=0..infinity);

NiM+SSV0ZXN0RzYiLUkmbGltaXRHNiRJKnByb3RlY3RlZEdGKUkoX3N5c2xpYkdGJTYkLCYqKEkmYWxwaGFHRiUiIiJJInNHRiVGLy1JJGV4cEdGKDYjLCQqJkYuRi9JInRHRiVGLyEiIkYvRjcqJkYuRi9GMEYvRi8vRjZJKWluZmluaXR5R0Yp

simplify(test);

NiMtSSZsaW1pdEc2JEkqcHJvdGVjdGVkR0YmSShfc3lzbGliRzYiNiQsJCooSSZhbHBoYUdGKCIiIkkic0dGKEYtLCYtSSRleHBHRiU2IywkKiZGLEYtSSJ0R0YoRi0hIiJGLUY2Ri1GLUY2L0Y1SSlpbmZpbml0eUdGJg==

pm:=serverf(t,alpha,s);

NiM+SSNwbUc2IiooSSZhbHBoYUdGJSIiI0kic0dGJSIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YlNiMsJComRidGKkkidEdGJUYqISIiRio=

ex:=int(t*pm,t=0..infinity);

NiM+SSNleEc2Ii1JJmxpbWl0RzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHRiU2JCwoKipJInNHRiUiIiItSSRleHBHRig2IywkKiZJJmFscGhhR0YlRi9JInRHRiVGLyEiIkYvRjVGL0Y2Ri9GNyomRi5GL0YwRi9GN0YuRi8vRjZJKWluZmluaXR5R0Yp

l:=[10.7,9.2,4.1,3.9,8.1,8.9,2.4,5.7,3.3,5.2];

NiM+SSJsRzYiNywkIiQyIiEiIiQiIyMqRikkIiNURikkIiNSRikkIiMiKUYpJCIjKilGKSQiI0NGKSQiI2RGKSQiI0xGKSQiI19GKQ==

n:=nops(l);

NiM+SSJuRzYiIiM1

L:=product(serverf(l[i],alpha,s),i=1..nops(l));

NiM+SSJMRzYiKjpJJmFscGhhR0YlIiM/SSJzR0YlIiM1LUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi5JKF9zeXNsaWJHRiU2IywkRickISQyIiEiIiIiIi1GLDYjLCRGJyQhIyMqRjRGNS1GLDYjLCRGJyQhI1RGNEY1LUYsNiMsJEYnJCEjUkY0RjUtRiw2IywkRickISMiKUY0RjUtRiw2IywkRickISMqKUY0RjUtRiw2IywkRickISNDRjRGNS1GLDYjLCRGJyQhI2RGNEY1LUYsNiMsJEYnJCEjTEY0RjUtRiw2IywkRickISNfRjRGNQ==

lnL:=unapply(ln(L),alpha,s);

NiM+SSRsbkxHNiJmKjYkSSZhbHBoYUdGJUkic0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkjbG5HNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjKjo5JCIjPzklIiM1LUkkZXhwR0YvNiMsJEY0JCEkMiIhIiIiIiItRjk2IywkRjQkISMjKkY+Rj8tRjk2IywkRjQkISNURj5GPy1GOTYjLCRGNCQhI1JGPkY/LUY5NiMsJEY0JCEjIilGPkY/LUY5NiMsJEY0JCEjKilGPkY/LUY5NiMsJEY0JCEjQ0Y+Rj8tRjk2IywkRjQkISNkRj5GPy1GOTYjLCRGNCQhI0xGPkY/LUY5NiMsJEY0JCEjX0Y+Rj9GJUYlRiU=

solve(diff(lnL(alpha,s),alpha)=0,alpha);

NiMkIis/RC5fSyEjNQ==

restart;l:=[3.15,2.93,2.87,3.21,3.04,2.96,2.79,3.06,2.98,2.81];

NiM+SSJsRzYiNywkIiQ6JCEiIyQiJCRIRikkIiQoR0YpJCIkQCRGKSQiJC8kRikkIiQnSEYpJCIkeiNGKSQiJDEkRikkIiQpSEYpJCIkIkdGKQ==

n:=nops(l);

NiM+SSJuRzYiIiM1

mu:=mittelwert(l);

NiM+SSNtdUc2IiQiKysrKyEpSCEiKg==

sig:=varStich(l);

NiM+SSRzaWdHNiIkIisrKys9PCEjNg==

sig2:=sig^2;

NiM+SSVzaWcyRzYiJCIrK1NfXkghIzg=

mu:=mittelwert(l);

NiM+SSNtdUc2IiQiKysrKyEpSCEiKg==

sig:=varGesamt(l);

NiM+SSRzaWdHNiIkIisqKSkpKSkzPiEjNg==

sig2:=sig^2;

NiM+SSVzaWcyRzYiJCIrInpjUWskISM4

sig2:=0.0121;

NiM+SSVzaWcyRzYiJCIkQCIhIiU=

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIkIisrKysrNiEjNQ==

xm:=mittelwert(l);

NiM+SSN4bUc2IiQiKysrKyEpSCEiKg==

n:=nops(l);

NiM+SSJuRzYiIiM1

ga:=0.975;

NiM+SSNnYUc2IiQiJHYqISIk

c:=fsolve(2*norF(0,1,x)-1=ga,x);

NiM+SSJjRzYiJCIrYEZTVEEhIio=

muMin:=evalf(xm-(c*sig)/sqrt(n));

NiM+SSZtdU1pbkc2IiQiKyVvSz8hSCEiKg==

muMax:=evalf(xm+(c*sig)/sqrt(n));

NiM+SSZtdU1heEc2IiQiKzt0J3owJCEiKg==

restart;schwarz:=1^2*Pi;

NiM+SShzY2h3YXJ6RzYiSSNQaUdJKnByb3RlY3RlZEdGJw==

gesamt:=5^2*Pi;

NiM+SSdnZXNhbXRHNiIsJEkjUGlHSSpwcm90ZWN0ZWRHRigiI0Q=

p:=schwarz/gesamt;

NiM+SSJwRzYiIyIiIiIjRA==

f:=(n,p)->p*(1-p)^(n-1);

NiM+SSJmRzYiZio2JEkibkdGJUkicEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JSIiIiksJkYvRi9GLiEiIiwmOSRGL0YyRi9GL0YlRiVGJQ==

muX:=evalf(int(x*f(x,1/25),x=0..infinity));

NiM+SSRtdVhHNiIkIitZK00rRCEiKQ==

muX:=evalf(sum(x*f(x,p),x=1..infinity));

NiM+SSRtdVhHNiIkIiNEIiIh

restart;

muZ:=320*0.15;

NiM+SSRtdVpHNiIkIiUrWyEiIw==

muA:=80;

NiM+SSRtdUFHNiIiIyEp

muB:=40;

NiM+SSRtdUJHNiIiI1M=

sig2Z:=320*0.15*(1-0.15);

NiM+SSZzaWcyWkc2IiQiJyshMyUhIiU=

sigZ:=sqrt(sig2Z);

NiM+SSVzaWdaRzYiJCIrcHhbKFEnISIq

sigA:=22;

NiM+SSVzaWdBRzYiIiNB

sigB:=22;

NiM+SSVzaWdCRzYiIiNB

mu:=muZ+muA+muB;

NiM+SSNtdUc2IiQiJitvIiEiIw==

sig2:=sigZ^2+sigA^2+sigB^2;

NiM+SSVzaWcyRzYiJCIrKyshKTM1ISIn

sig:=evalf(sqrt(sig2));

NiM+SSRzaWdHNiIkIiswNzt3SiEiKQ==

100*evalf(norF(mu,sig,150)-norF(mu,sig,90));

NiMkIis0IkhVeSMhIik=

restart;alpha1:=1.5;

NiM+SSdhbHBoYTFHNiIkIiM6ISIi

alpha2:=3;

NiM+SSdhbHBoYTJHNiIiIiQ=

fx:=(t)->alpha1*exp(-alpha1*t);

NiM+SSNmeEc2ImYqNiNJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSomSSdhbHBoYTFHRiUiIiItSSRleHBHRiU2IywkKiZGLUYuOSRGLiEiIkYuRiVGJUYl

plot(fx(x),x=0..10);

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

fy:=(t)->alpha2*exp(-alpha2*t);

NiM+SSNmeUc2ImYqNiNJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSomSSdhbHBoYTJHRiUiIiItSSRleHBHNiRJKnByb3RlY3RlZEdGMkkoX3N5c2xpYkdGJTYjLCQqJkYtRi45JEYuISIiRi5GJUYlRiU=

plot(fy(x),x=0..10);

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

fz:=(t)->fx(t)*fy(t);

NiM+SSNmekc2ImYqNiNJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSomLUkjZnhHRiU2IzkkIiIiLUkjZnlHRiVGL0YxRiVGJUYl

plot(fz(x),x=0..10);

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

Fz:=(t)->int(fz(v),v=0..infinity)-int(fz(v),v=0..t);

NiM+SSNGekc2ImYqNiNJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmLUkkaW50R0YlNiQtSSNmekdGJTYjSSJ2R0YlL0YzOyIiIUkpaW5maW5pdHlHSSpwcm90ZWN0ZWRHRjgiIiItRi42JEYwL0YzO0Y2OSQhIiJGJUYlRiU=

100*Fz(1);

NiMkIitdJyoqMzYiISIq

restart;l:=[47,53,51,51,58,46,44,49,54,58,61,44,45,49,55];

NiM+SSJsRzYiNzEiI1oiI2AiI15GKSIjZSIjWSIjVyIjXCIjYUYqIiNoRiwiI1hGLSIjYg==

sig2:=8;

NiM+SSVzaWcyRzYiIiIp

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIsJCokIiIjIyIiIkYoRig=

xm:=mittelwert(l);

NiM+SSN4bUc2IiIjXg==

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.99;

NiM+SSNnYUc2IiQiIyoqISIj

c:=fsolve(2*norF(0,1,x)-1=ga,x);

NiM+SSJjRzYiJCIrZiRIZWQjISIq

muMin:=evalf(xm-(c*sig)/sqrt(n));

NiM+SSZtdU1pbkc2IiQiK0AhKSk9IlwhIik=

muMax:=evalf(xm+(c*sig)/sqrt(n));

NiM+SSZtdU1heEc2IiQiK3o+NilHJiEiKQ==

xm:=mittelwert(l);

NiM+SSN4bUc2IiIjXg==

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.99;

NiM+SSNnYUc2IiQiIyoqISIj

# Varianz der Grundgesamtheits2:=1/(n-1)*sum((l[i]-xm)^2,i=1..n);

NiM+SSNzMkc2IiMiJDAjIiIo

s:=sqrt(s2);

NiM+SSJzRzYiLCQqJCIlTjkjIiIiIiIjI0YqIiIo

c:=fsolve(2*tF(x,n-1)-1=ga,x);

NiM+SSJjRzYiJCIrY0YlbyhIISIq

muMin:=evalf(xm-((c*s)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiK0dHMCVvJSEiKQ==

muMin:=evalf(xm+((c*s)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiK3NyJWZeJiEiKQ==

sig2:=8;

NiM+SSVzaWcyRzYiIiIp

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIsJCokIiIjIyIiIkYoRig=

xm:=mittelwert(l);

NiM+SSN4bUc2IiIjXg==

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.99;

NiM+SSNnYUc2IiQiIyoqISIj

c:=fsolve(2*norF(0,1,x)-1=ga,x);

NiM+SSJjRzYiJCIrZiRIZWQjISIq

l:=(n)->2*(c*sig)/sqrt(n);

NiM+SSJsRzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqKEkiY0dGJSIiIkkkc2lnR0YlRi8tSSVzcXJ0RzYkSSpwcm90ZWN0ZWRHRjRJKF9zeXNsaWJHRiU2IzkkISIiIiIjRiVGJUYl

laenge:=solve(l(x)=2,x);

NiM+SSdsYWVuZ2VHNiIkIis4diJ6SSYhIik=

xm:=mittelwert(l);

NiM+SSN4bUc2IiIjXg==

n:=nops(l);

NiM+SSJuRzYiIiM6

ga:=0.99;

NiM+SSNnYUc2IiQiIyoqISIj

s2:=1/(n-1)*sum((l[i]-xm)^2,i=1..n);

NiM+SSNzMkc2IiMiJDAjIiIo

c1:=fsolve(chiF(x,n-1)=(1-ga)/2,x);

NiM+SSNjMUc2IiQiK2NcbnVTISIq

c2:=fsolve(chiF(x,n-1)=(1+ga)/2,x);

NiM+SSNjMkc2IiQiK2lcJD44JCEiKQ==

minSig2:=((n-1)*s2)/c2;

NiM+SShtaW5TaWcyRzYiJCIrdFs0NDghIik=

maxSig2:=((n-1)*s2)/c1;

NiM+SShtYXhTaWcyRzYiJCIrSV9AMTUhIig=

minSig:=sqrt(minSig2);

NiM+SSdtaW5TaWdHNiIkIis4Ozk9TyEiKg==

maxSig:=sqrt(maxSig2);

NiM+SSdtYXhTaWdHNiIkIissRzUuNSEiKQ==

restart;maxW:=(v,m,T,k)->4*Pi*(m/(2*Pi*k*T))*v^2*exp(-((m*v^2)/(2*k*T)));

NiM+SSVtYXhXRzYiZio2JkkidkdGJUkibUdGJUkiVEdGJUkia0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKjIiIiMiIiJJI1BpR0kqcHJvdGVjdGVkR0YzRjE5JUYxRjIhIiI5J0Y1OSZGNTkkRjAtSSRleHBHRiU2IywkKipGNEYxRjhGMEY2RjVGN0Y1I0Y1RjBGMUYlRiVGJQ==

l:=[solve(diff(maxW(v,m,T,k),v)=0,v)];

NiM+SSJsRzYiNyUiIiEqKEkibUdGJSEiIiIiIyMiIiJGKyooRilGLUkia0dGJUYtSSJUR0YlRi1GLCwkRihGKg==

res:=l[2];

NiM+SSRyZXNHNiIqKEkibUdGJSEiIiIiIyMiIiJGKSooRidGK0kia0dGJUYrSSJUR0YlRitGKg==

# kontinuierlichpm:=maxW(v,m,T,k);

NiM+SSNwbUc2IiwkKixJIm1HRiUiIiJJImtHRiUhIiJJIlRHRiVGK0kidkdGJSIiIy1JJGV4cEc2JEkqcHJvdGVjdGVkR0YySShfc3lzbGliR0YlNiMsJCoqRihGKUYtRi5GKkYrRixGKyNGK0YuRilGLg==

ex:=int(v*pm,v=0..infinity);

NiM+SSNleEc2Ii1JJmxpbWl0RzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHRiU2JCwkKiYsKCooLUkkZXhwR0YoNiMsJCoqSSJtR0YlIiIiSSJ2R0YlIiIjSSJrR0YlISIiSSJUR0YlRjojRjpGOEY2RjVGNkY3RjhGNiooRjlGNkY7RjZGMEY2RjgqJkY5RjZGO0Y2ISIjRjZGNUY6Rj8vRjdJKWluZmluaXR5R0Yp

# fuer v^2ex:=int(v^2*pm,v=0..infinity);

NiM+SSNleEc2Ii1JJmxpbWl0RzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHRiU2JCooSSJtR0YlISIiLCgqKkkidkdGJSIiJC1JJGV4cEdGKDYjLCQqKkYtIiIiRjEiIiNJImtHRiVGLkkiVEdGJUYuI0YuRjlGOEYtRjgqKEYtRjhGOkYuRjtGLiNGOEY5ISIjKixGOkY4RjtGOEYxRjhGM0Y4Rj1GPiEiJyosRjpGOEY7RjhJI1BpR0YpRj5GOUY+LUkkZXJmR0YoNiMsJCooRjlGPkY9Rj5GMUY4Rj5GOEYyRjhGPUY8L0YxSSlpbmZpbml0eUdGKQ==

# diskreted:=sum(v*pm,v=0..infinity);

NiM+SSNlZEc2Ii1JJHN1bUc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliR0YlNiQsJCosSSJ2R0YlIiIkSSJtR0YlIiIiSSJrR0YlISIiSSJUR0YlRjMtSSRleHBHRig2IywkKipGMEYxRi4iIiNGMkYzRjRGMyNGM0Y6RjFGOi9GLjsiIiFJKWluZmluaXR5R0Yp

l:=[v1,v2,v3,v4,v5];

NiM+SSJsRzYiNydJI3YxR0YlSSN2MkdGJUkjdjNHRiVJI3Y0R0YlSSN2NUdGJQ==

n:=nops(l);

NiM+SSJuRzYiIiIm

L:=Product(maxW(l[i],m,T,k),i=1..n);

NiM+SSJMRzYiLUkoUHJvZHVjdEc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliR0YlNiQsJCosSSJtR0YlIiIiSSJrR0YlISIiSSJUR0YlRjEmNydJI3YxR0YlSSN2MkdGJUkjdjNHRiVJI3Y0R0YlSSN2NUdGJTYjSSJpR0YlIiIjLUkkZXhwR0YoNiMsJCoqRi5GL0YzRjxGMEYxRjJGMSNGMUY8Ri9GPC9GOztGLyIiJg==

L:=simplify(L);

NiM+SSJMRzYiLCQqKkkibUdGJSIiJkkia0dGJSEiJkkiVEdGJUYrLUkoUHJvZHVjdEc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiQqJiY3J0kjdjFHRiVJI3YyR0YlSSN2M0dGJUkjdjRHRiVJI3Y1R0YlNiNJImlHRiUiIiMtSSRleHBHRi82IywkKipGKCIiIkY0Rj1GKiEiIkYsRkQjRkRGPUZDL0Y8O0ZDRilGQyIjSw==

lnL:=ln(L);

NiM+SSRsbkxHNiItSSNsbkc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliR0YlNiMsJCoqSSJtR0YlIiImSSJrR0YlISImSSJUR0YlRjEtSShQcm9kdWN0R0YoNiQqJiY3J0kjdjFHRiVJI3YyR0YlSSN2M0dGJUkjdjRHRiVJI3Y1R0YlNiNJImlHRiUiIiMtSSRleHBHRig2IywkKipGLiIiIkY3RkBGMCEiIkYyRkcjRkdGQEZGL0Y/O0ZGRi9GRiIjSw==

dLm:=diff(lnL,m)=0;

NiM+SSRkTG1HNiIvLCQqLCwmKipJIm1HRiUiIiVJImtHRiUhIiZJIlRHRiVGLi1JKFByb2R1Y3RHNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYkKiYmNydJI3YxR0YlSSN2MkdGJUkjdjNHRiVJI3Y0R0YlSSN2NUdGJTYjSSJpR0YlIiIjLUkkZXhwR0YyNiMsJCoqRisiIiJGN0ZARi0hIiJGL0ZHI0ZHRkBGRi9GPztGRiIiJkZGIiRnIioqRitGS0YtRi5GL0YuLUkkU3VtR0YyNiQsJCouLUYxNiQqJiZGODYjSSRpMXxpckdGJUZALUZCNiMsJCoqRitGRkZWRkBGLUZHRi9GR0ZIRkYvRlg7RkYsJkY/RkZGR0ZGRkYtRjE2JEZVL0ZYOywmRj9GRkZGRkZGS0ZGRjdGLEYtRkdGL0ZHRkFGRkZIRklGRiIjS0ZGRitGLkYtRktGL0ZLRjBGRyNGRkZfbyIiIQ==

dLT:=diff(lnL,T)=0;

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

simplify(dLm);

Error, (in thaw) too many levels of recursion

simplify(dLT);

Error, (in thaw) too many levels of recursion

restart;l:=[14,21,20,24,10,16,28,22,16,28];

NiM+SSJsRzYiNywiIzkiI0AiIz8iI0MiIzUiIzsiI0ciI0FGLEYt

# geometrische verteilung # beschreibt n-1 Misserfolge bis Erfolg im n-ten Versuch # mit Erfolgs'wkeit pf:=(n,p)->p*(1-p)^(n-1);

NiM+SSJmRzYiZio2JEkibkdGJUkicEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JSIiIiksJkYvRi9GLiEiIiwmOSRGL0YyRi9GL0YlRiVGJQ==

L:=product(f(l[i],p),i=1..nops(l));

NiM+SSJMRzYiKiZJInBHRiUiIzUsJiIiIkYqRichIiIiJCo9

lnL:=unapply(ln(L),p);

NiM+SSRsbkxHNiJmKjYjSSJwR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSNsbkc2JEkqcHJvdGVjdGVkR0YvSShfc3lzbGliR0YlNiMqJjkkIiM1LCYiIiJGNkYzISIiIiQqPUYlRiVGJQ==

plot(lnL(x),x=-100..1);

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

p:=100*fsolve(diff(lnL(p),p)=0,p);

NiM+SSJwRzYiJCIrR2M3RF0hIio=

p:=100*evalf(1/mittelwert(l));

NiM+SSJwRzYiLCQqJC1JK21pdHRlbHdlcnRHRiU2IzcsIiM5IiNAIiM/IiNDIiM1IiM7IiNHIiNBRjFGMiEiIiIkKyI=

restart;muA:=700;

NiM+SSRtdUFHNiIiJCso

muB:=1070;

NiM+SSRtdUJHNiIiJXE1

sigA:=110;

NiM+SSVzaWdBRzYiIiQ1Ig==

sigB:=180;

NiM+SSVzaWdCRzYiIiQhPQ==

mu:=muA+muB;

NiM+SSNtdUc2IiIlcTw=

sig2:=sigA^2+sigB^2;

NiM+SSVzaWcyRzYiIiYrWCU=

sig:=evalf(sqrt(sig2));

NiM+SSRzaWdHNiIkIis2Ql00QCEiKA==

restart;l:=[12.3,11.0,8.9,8.6,9.4,13.2,10.8,9.9,7.4,10.2,6.3];

NiM+SSJsRzYiNy0kIiRCIiEiIiQiJDUiRikkIiMqKUYpJCIjJylGKSQiIyUqRikkIiRLIkYpJCIkMyJGKSQiIyoqRikkIiN1RikkIiQtIkYpJCIjakYp

n:=nops(l);

NiM+SSJuRzYiIiM2

mu:=mittelwert(l);

NiM+SSNtdUc2IiQiKz09PT0pKiEiKg==

sig:=varGesamt(l);

NiM+SSRzaWdHNiIkIitpamokMyUhIio=

ga:=0.9;

NiM+SSNnYUc2IiQiIiohIiI=

xm:=mittelwert(l);

NiM+SSN4bUc2IiQiKz09PT0pKiEiKg==

c:=fsolve(2*tF(x,n-1)-1=0.9,x);

NiM+SSJjRzYiJCIrQzZZNz0hIio=

muMin:=evalf(xm-((c*sig)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiK2VnYydlKCEiKg==

muMin:=evalf(xm+((c*sig)/sqrt(n)));

NiM+SSZtdU1pbkc2IiQiK2Uoelw/IiEiKQ==

c1:=fsolve(chiF(x,n-1)=(1-ga)/2,x);

NiM+SSNjMUc2IiQiK08iKkhTUiEiKg==

c2:=fsolve(chiF(x,n-1)=(1+ga)/2,x);

NiM+SSNjMkc2IiQiKzBRcUk9ISIp

minSig2:=((n-1)*sig)/c2;

NiM+SShtaW5TaWcyRzYiJCIrI1JQMUIjISIq

maxSig2:=((n-1)*sig)/c1;

NiM+SShtYXhTaWcyRzYiJCIrWHNQTzUhIik=

minSig:=sqrt(minSig2);

NiM+SSdtaW5TaWdHNiIkIitfPWAkXCIhIio=

maxSig:=sqrt(maxSig2);

NiM+SSdtYXhTaWdHNiIkIitjOEc+SyEiKg==