Lösungen / Statistik 2/13

Remove["Global`*"]

1.

a

alpha = 0.01;
f[z_, 
          n_] := Gamma[(n + 1)/
                2]/(Sqrt[n Pi] Gamma[n/2])/(1 + 
                z^2/n)^((n + 1)/2);
{"c", 
      c = c /. FindRoot[
              alpha/2 == 
                Evaluate[1 - Integrate[f[u, 20], {u, -Infinity, c}]], {c, 
                2}] // Chop, "Interv", {-c, +c}}

Ii[s_, n_, μ0_] := {-c*s/Sqrt[n] + μ0, 
        c*s/Sqrt[n] + μ0}

Ii[1.2, 20, 128]

{-2.84534*1.2/Sqrt[20] + 128, 
      2.84534*1.2/Sqrt[20] + 128}

127.3  in  iI,  H0  o.k.

b

alpha = 0.001;
f[z_, 
          n_] := Gamma[(n + 1)/
                2]/(Sqrt[n Pi] Gamma[n/2])/(1 + 
                z^2/n)^((n + 1)/2);
{"c", 
      c = c /. FindRoot[
              alpha/2 == 
                Evaluate[
                  1 - Integrate[f[u, 100], {u, -Infinity, c}]], {c, 2}] // 
          Chop, "Interv", {-c, +c}}

Ii[s_, n_, μ0_] := {-c*s/Sqrt[n] + μ0, 
        c*s/Sqrt[n] + μ0}

Ii[2, 100, 400]

406.78  not in  iI,  H1 o.k.

2.

alpha = 0.001;
f[z_, 
          n_] := Gamma[(n + 1)/
                2]/(Sqrt[n Pi] Gamma[n/2])/(1 + 
                z^2/n)^((n + 1)/2);
{"c", 
      c = c /. FindRoot[
              alpha == 
                Evaluate[
                  Integrate[f[u, 100], {u, -Infinity, c}]], {c, -2}] // 
          Chop, "Interv", {-c, Infinity}}

Ii[s_, n_, μ0_] := {c*s/Sqrt[n] + μ0, 
        Infinity*s/Sqrt[n] + μ0}

Ii[2, 100, 400]

406.78  in  iI,  H1 o.k.