Lösungen/Solutions/F2S2Ue/Ex03

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

Ueb/Ex 1      W

f[ν_, μ_, σ_] := 
        1/(σ Sqrt[2 Pi]) E^(-1/
                  2*(ν - μ)^2/σ^2);
F[x_, μ_, σ_] := 
      Evaluate[Integrate[
          f[ν, μ, σ], {ν, -Infinity, x}]]

a

Plot[f[ν, 0, 1], {ν, -5, 5}];

Plot[F[x, 0, 1], {x, -5, 5}];

Plot[{f[x, 0, 1], F[x, 0, 1]}, {x, -5, 5}];

b

Plot[{f[x, 0, 2], F[x, 0, 2]}, {x, -5, 5}];

c

Plot[{f[x, 0, 1/2], F[x, 0, 1/2]}, {x, -5, 5}];

d

Plot[{f[x, 3, 1], F[x, 3, 1]}, {x, -5, 8}, 
        PlotRange -> {0, 1}];

d

Plot[{f[x, 3, 2], F[x, 3, 2]}, {x, -5, 8}, 
        PlotRange -> {0, 1}];

e

Plot[{f[x, 3, 1/2], F[x, 3, 1/2]}, {x, -5, 8}, 
        PlotRange -> {0, 1}];

Ueb/Ex 2      W

Plot[{f[x, 30, 0.02], F[x, 30, 0.02]}, {x, 29.8, 30.2}, 
        PlotRange -> {0, 20}];

Plot[{F[x, 30, 0.02]}, {x, 29.9, 30.1}];

Ausschuss  / Rebut   ( % ) :

((1 - F[30 + 0.03, 30, 0.02])  +  
        F[30 - 0.03, 30, 0.02])

((1 - F[30 + 0.03, 30, 0.02]) + F[30 - 0.03, 30, 0.02]) *100 // 
      N

Ueb/Ex 3      W

a

Remove["Global`@*"]

n = 400;  p = 0.07;  m = 10;

<< Statistics`DiscreteDistributions`

bdist[n_] := BinomialDistribution[n, p]

pdf[n_, x_] := PDF[bdist[n], x];
cdf[n_, m_] := CDF[bdist[n], m];

1 - cdf[n, m - 1]

Sum[pdf[n, x], {x, m, n}]

b

f[ν_, μ_, σ_] := 
        1/(σ Sqrt[2 Pi]) E^(-1/
                  2*(ν - μ)^2/σ^2);
F[x_, μ_, σ_] := 
      Evaluate[Integrate[
          f[ν, μ, σ], {ν, -Infinity, x}]]

q = 1 - p;  μ = n*p;  σ = Sqrt[μ*q];

1 - F[10, μ, σ] // N

1 - F[9, μ, σ] // N

1 - F[9.5, μ, σ] // N