Verschiebung nach rechts

Glockenfunktion

angepasste Skalierung

0

\mu

1

\sigma

Binomialverteilung

\varphi(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}

z = \frac{x - μ}{σ}

σ \cdot P(X = x) \; \textcolor{black}{\approx} \; \textcolor{orange}{φ(z)}

1

-1

μ

μ+σ

μ-σ

-1

1

Variation

V1 = BinomialDist(20, 0.25)
gU: -0.1
gO: 0.5
n = 60 (slider from 1 to 100, step 1)
p = 0.25 (slider from 0.01 to 0.99, step 0.01)
gn20p025 = Sequence(i - 0.5, i, 0, n + 1)
hn20p025 = Sequence(BinomialDist[n, p, k, false], k, 0, n)
H = Histogram(gn20p025, hn20p025)
μ: (n * p)
v = 14.85 (slider from 0 to μ, step 0.01)
gvn20p025 = Zip(i - μ, i, gn20p025)
σ: sqrt(((n * p) * (1 - p)))
gvsn20p025 = Zip(i / σ, i, gvn20p025)
Hvsn20p025 = Histogram(gvsn20p025, hn20p025)
hsn20p025 = Zip((i * σ), i, hn20p025)
Hvssn20p025 = Histogram(gvsn20p025, hsn20p025)
StreckeE = Segment((0, 0), (μ, 0))
E = Point(StreckeE)
S: E + (σ, 0)
Text1: "" + (μ - v) + ""
v': μ - v
grenzen = Sequence(i - 0.5, i, 0, n + 1)
grenzenverschoben = Zip(i - v, i, gn20p025)
hoehen = Sequence(BinomialDist[n, p, k, false], k, 0, n)
Hv = Histogram(grenzenverschoben, hoehen)
s = 3.35 (slider from smin to smax, step 0.01)
smin = Min(1, σ)
smax = Max(1, σ)
hoehengedehnt = Zip((i * s), i, hoehen)
grenzenverschobengestaucht = Zip(i / s, i, grenzenverschoben)
Hvs = Histogram(grenzenverschobengestaucht, hoehengedehnt)
φ(x) = (1 / sqrt((2 * pi)) * ℯ^((-1 / 2 * x^(2))))
bGlockenkurve = true
bSkalierung = true
xPunkte = Sequence((i, 0), i, 0, n)
X = Point(xPunkte)
xRechteckvs = Polygon({(grenzenverschobengestaucht(x(X) + 1), 0), (grenzenverschobengestaucht(x(X) + 2), 0), (grenzenverschobengestaucht(x(X) + 2), hoehengedehnt(x(X) + 1)), (grenzenverschobengestaucht(x(X) + 1), hoehengedehnt(x(X) + 1))})
xRechteck = Polygon({(grenzen(x(X) + 1), 0), (grenzen(x(X) + 2), 0), (grenzen(x(X) + 2), hoehen(x(X) + 1)), (grenzen(x(X) + 1), hoehen(x(X) + 1))})
Text5: "Verschiebung nach links: " + v + ""
Text6: "Stauchen / Strecken mit Faktor: " + s + ""
Text2: "μ: " + μ + ""
Text10: "σ: " + σ + ""
gL: -5
k: x(X)
Text13: "x = " + k + ""
Z: ((k - v) / s, 0)
Text12: "P(X =x) \approx " + (LaTeX[hoehen(k + 1)]) + ""
gE = Ray(E, E + (0, 1))
gS1 = Ray((x(E) + σ, 0), (x(E) + σ, 1))
gS2 = Ray((x(E) - σ, 0), (x(E) - σ, 1))
gE' = Ray(((x(E) - v) / s, 0), ((x(E) - v) / s, 1))
gS1' = Ray(((x(E) - v + σ) / s, 0), ((x(E) - v + σ) / s, 1))
gS2' = Ray(((x(E) - v - σ) / s, 0), ((x(E) - v - σ) / s, 1))
E1: (1, 0.5) - (Corner[Text16, 4] - Corner[Text16, 1])
E2: (-1, 0.5) - (Corner[Text17, 4] - Corner[Text17, 1])
bTexth2: x(Corner[Texth2, 2] - Corner[Texth2, 1])
bTexth1: x(Corner[Texth1, 2] - Corner[Texth1, 1])
bVariation = true
gR = If(bSkalierung, μ + (4 * σ), 35)