Lösungen/Solutions/F2S2Ue/Ex09

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A=Anhang/Annexe/Appendice

Ueb/Ex 1      W

Remove["Global`@*"]

Idee/ Idée:

α = 0.001;  
    n = 100;   μ0 = 200;  σ = 4;

fR[α_] := 
        FindRoot[
          1/(Sqrt[2 Pi]) Integrate[
                E^(-x^2/2), {x, -c, c}] == 
            1 - α, {c, 1}];

c1[c_] := c /. fR[α];  c1[c]

g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);

solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
cU1[n, μ, σ]

solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
cO1[n, μ, σ]

Programm

α = 0.001;  n = 10;   μ0 = 200;  σ = 4; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}

α = 0.001;  n = 100;   μ0 = 200;  σ = 4; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}

α = 0.001;  n = 1000;   μ0 = 200;  σ = 4; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}

α = 0.001;  n = 100;   μ0 = 200;  σ = 0.1; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}

Ueb/Ex 2      W

β = 0.01;  α = β;   n = 100;   μ0 = 
      200;  σ = 4; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}

α = 0.001;  n = 100;   μ0 = 200;  σ = 4; 
    fR[α_] := 
      FindRoot[1/(Sqrt[2 Pi]) Integrate[
              E^(-x^2/2), {x, -c, c}] == 1 - α, {c, 
          1}];
c1[c_] := c /. fR[α];
g1[
          c_] := (-c1[c] == 
            Sqrt[n] (cU - μ0)/σ);
g2[
          c_] := (c1[c] == 
            Sqrt[n] (cO - μ0)/σ);
solv1 = Solve[g1[c], {cU}] //  Flatten;
cU1[n_, μ_, σ_] := 
        cU /. solv1;
solv2 = Solve[g2[c], {cO}] //  Flatten;
cO1[n_, μ_, σ_] := 
        cO /. solv2;
{cU1[n, μ, σ], cO1[n, μ, σ]}