Vielfache

$\mu$

\mu

\text{Binomialverteilung:}

\mu-\sigma

\mu+\sigma

E(X)

$\sigma(X)$

n = 13 (slider from 4 to 20, step 1)
xPunkte = Sequence((i, 0), i, 0, n)
K = Point(xPunkte)
k: x(K)
p = 0.5 (slider from 0 to 1, step 0.01)
r = 1 (slider from 1 to 3, step 1)
EX: (n * p)
SX: sqrt(((n * p) * (1 - p)))
d: EX + (r * SX)
d1: floor(d)
c: EX - (r * SX)
c1: ceil(c)
Verteilung = BinomialDist(n, p)
O = 0.5 (slider from -5 to 5)
U = -0.07 (slider from -5 to 5)
a: EX - SX
bink = BinomialDist(n, p, {k})
b: EX + SX
xHistogramm = Sequence(i, i, a, b)
yHistogramm = Sequence(((nCr[n, i] * p^(i)) * (1 - p)^(n - i)), i, k, k)
HistogrammIntervall = BarChart(xHistogramm, yHistogramm)
xPunkteIntervall = Sequence((i, 0), i, k, k)
VerteilungIntervall = Zip(Polygon[{P + (0.5, 0), P + (0.5, h), P + (-0.5, h), P + (-0.5, 0)}], P, xPunkteIntervall, h, yHistogramm)
v: (-0.2, -0.05)
binab = BinomialDist(n, p, Sequence[i, i, c1, d1])
xWerte = Sequence(i, i, 0, n)
yWerte = Sequence(((nCr[n, i] * p^(i)) * (1 - p)^(n - i)), i, 0, n)
P = 1 (slider from -5 to 5)
h = 1 (slider from -5 to 5)
werte = 1 (slider from -5 to 5)
VerteilungX = Zip(Polygon[{P + (0.5, 0), P + (0.5, h), P + (-0.5, h), P + (-0.5, 0)}], P, xPunkte, h, yWerte)
m: x = EX
ga: x = c
gb: x = d
yV = 0.45 (slider from -5 to 5)
A: (c, yV)
M: (EX, yV)
B: (d, yV)
u = Vector(A, M)
w = Vector(M, A)
e = Vector(M, B)
f = Vector(B, M)
kSX: (0, -0.01)
vB: (0, 0.04)
vA: (0, -0.04)
L: ((-n)) / 10
R: n + n / 10
Text8: "k = " + k + ""
Balken = Polygon({K + (0.5, 0), K + (0.5, bink), K + (-0.5, bink), K + (-0.5, 0)})
Text2: "
\text{Wahrscheinlichkeit: P(X = " + (LaTeX[k]) + ") = " + (LaTeX[bink]) + ""
Produkte = Sequence((i * yWerte(i + 1)), i, 0, k)
EXk = Sum(Produkte)
bEX = true
bSA = true
Text4: "\text{Erwartungswert:} \\

\underbrace{E(X)}_{\mu} = \underbrace{\begin{array}{lcr} & 0\cdot P(X=0) \\+ & \dots \\ + & " + (LaTeX[n]) + "\cdot P(X=" + (LaTeX[n]) + ") \end{array}}_{0\dots" + (LaTeX[k]) + ": " + (LaTeX[EXk]) + "} = " + (LaTeX[EX]) + ""
Abweichungen = Sequence(((i - EX)^(2) * yWerte(i + 1)), i, 0, k)
SAk = Sum(Abweichungen)
Text5: "\text{Standardabweichung:} \\\underbrace{\sigma(X)}_{\sigma} = \underbrace{\sqrt{\begin{array}{lcr} & (0-\mu)^2\cdot P(X=0) \\+ & \dots \\+ & (" + (LaTeX[n]) + "-\mu)^2\cdot P(X=" + (LaTeX[n]) + ")\end{array}}}_{0\dots" + (LaTeX[k]) + ": \sqrt{" + (LaTeX[SAk]) + "}} = " + (LaTeX[SX]) + ""