restart: with(LinearAlgebra): with(plots):

Warning, the name changecoords has been redefined

N:=<14, 21, 20, 24, 10, 16, 28, 22, 16, 28>: n:=Dimension(N);

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L:=unapply( mul( (1-Theta)^(N[i]-1), i=1..n), Theta);

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## Funktion mit ln() erweitern L2:=Theta->10 * ln(Theta) + 189 * ln(1 - Theta);

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# Maximum suchen d:=diff(L2,Theta); solve(d=0,Theta);

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plot(L2(Theta),Theta=0..0.2);

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

restart: with(LinearAlgebra): with(stats):X:=[100, 96, 98, 102, 97, 105, 98, 95, 101, 96]: n:=nops(X); sigNiveau:=0.90;

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## gesch\344tzter Mittelwert mu:=evalf( add(X[i],i=1..n)/n ); mu:=evalf(describe[mean](X));

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## Stichprobenvarianz varX:=evalf( (1/(n-1)) * Sum( '(X[i]-mu)^2' , 'i'=1..n) ); varX:=evalf(describe[variance[1]](X));

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## empirische Standartabweichung #sigma:=evalf(sqrt(varX)); sigma:=sqrt(varX); #sigma:=evalf(describe[standarddeviation[1]](X));

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## Quantil t-Student printf("Siehe Tabelle Student-Verteilung: alpha=%f, n=%d", 1 - (1 - sigNiveau) / 2, n - 1); ## c findet man in der Tabelle im Stochastik-Buch (Student-Verteilung) # c:=1.833; ## <-- Tabelleneintrag hier einf\374llen ## Tabelle von Maple verwenden c:=statevalf[icdf, studentst[n - 1]](1 - (1 - sigNiveau) / 2);

Siehe Tabelle Student-Verteilung: alpha=0.950000, n=9

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## Vertrauensintervall Mittelwert printf("Untere Vertrauensintervallgrenze: %f\n", evalf( mu-c*sigma/sqrt(n) )); #untereVertrauensintervallgrenze:=evalf( mu-c*sigma/sqrt(n) ); printf("Obere Vertrauensintervallgrenze: %f\n", evalf( mu+c*sigma/sqrt(n) ));

Untere Vertrauensintervallgrenze: 96.970965 Obere Vertrauensintervallgrenze: 100.629035

## Quantil Chi-Square printf("Siehe Tabelle Chi-Quadrat-Verteilung: alpha=%f, n=%d", (1 - sigNiveau) / 2, n - 1); ## MU findet man in der Tabelle im Stochastik-Buch (Chi-Quadrat-Verteilung) MU:= 3.325 ; ## <-- Tabelleneintrag hier einf\374llen ## Tabelle von Maple verwenden MU:=statevalf[icdf, chisquare[n - 1]]((1 - sigNiveau) / 2); printf("Siehe Tabelle Chi-Quadrat-Verteilung: alpha=%f, n=%d", 1 - (1 - sigNiveau) / 2, n - 1); ## mu findet man in der Tabelle im Stochastik-Buch (Chi-Quadrat-Verteilung) # mu:= 16.92 ; ## <-- Tabelleneintrag hier einf\374llen ## Tabelle von Maple verwenden mu:=statevalf[icdf, chisquare[n - 1]](1 - (1 - sigNiveau) / 2);

Siehe Tabelle Chi-Quadrat-Verteilung: alpha=0.050000, n=9NiM+SSNNVUc2IiQiJURMISIkNiM+SSNNVUc2IiQiK1ZHNkRMISIqSiehe Tabelle Chi-Quadrat-Verteilung: alpha=0.950000, n=9NiM+SSNtdUc2IiQiK2d4Kj1wIiEiKQ==

## Vertrauensintervall Standartabweichung # printf("Min Standartabweichung: %f\n", ); # printf("Max Standartabweichung: %f\n", );