Vielfache

\text{Bernoulli-Kette:}

E(X)

$\sigma(X)$

Trichter

\text{Sicherheitswahrscheinlichkeit:}

n = 400 (slider from 50 to maxN, step 50)
p = 0.5 (slider from 0 to 1, step 0.01)
r = 2 (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 = 1.1 (slider from -5 to 5, step 0.1)
U = -0.1 (slider from -5 to 5, step 0.1)
a: EX - SX
b: EX + SX
v: (-0.2, -0.05)
binab = BinomialDist(n, p, Sequence[i, i, c1, d1])
P = 1 (slider from -5 to 5, step 0.1)
h(x) = If[x ≥ 0, p]
werte = 1 (slider from -5 to 5, step 0.1)
yV = 0.45 (slider from -5 to 5, step 0.1)
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)
bEX = true
bSA = true
Text4: "\text{Erwartungswert:} \\

\underbrace{E(X)}_{\mu} = n \cdot p = " + (LaTeX[EX]) + ""
Text5: "\text{Standardabweichung:} \\\underbrace{\sigma(X)}_{\sigma} =  \sqrt{n \cdot p \cdot(1-p)} = " + (LaTeX[SX]) + ""
faktorSigma = If(r ≟ 1, 1.64, If[r ≟ 2, 1.96, 2.58])
Sigma = 1 (slider from -5 to 5, step 0.1)
SigmaYY: Sigma
sigmaDurchN: SX / n
prognoseintervallLinks: p - (faktorSigma * sigmaDurchN)
prognoseintervallRechts: p + (faktorSigma * sigmaDurchN)
maxN = 1000 (slider from -5 to 2000, step 0.1)
L = -50 (slider from -50 to 5, step 0.1)
R: maxN + 50
PLinks: (n, prognoseintervallLinks)
PRechts: (n, prognoseintervallRechts)
Prozentangabe = If(r ≟ 1, "90%", If[r ≟ 2, "95%", "99%"])
faktorWurzelN: (faktorSigma * sqrt((p * (1 - p))))
prognoseAbsLinks: EX - (faktorSigma * SX)
prognoseAbsRechts: EX + (faktorSigma * SX)
h1(x) = p - (faktorWurzelN * 1 / sqrt(x))
h2(x) = p + (faktorWurzelN * 1 / sqrt(x))
g = Segment(PLinks, PRechts)
i = true
Text9: "\text{\textcolor[rgb]{0,0.39,0}{" + (LaTeX[Prozentangabe]) + "}-\textcolor{red}{Prognoseintervall\ für\ die\ relative\ Trefferhäufigkeit\ h=\frac{X}{n}:}}\\
\underbrace{\frac{\mu}{n} - " + (LaTeX[faktorSigma]) + "\frac{\sigma}{n}}_{p - " + (LaTeX[faktorWurzelN]) + "\cdot\frac{1}{\sqrt{n}}} = \textcolor{red}{ " + (LaTeX[prognoseintervallLinks]) + "
\leq \frac{X}{n} \leq " + (LaTeX[prognoseintervallRechts]) + "} = \underbrace{\frac{\mu}{n} + " + (LaTeX[faktorSigma]) + "\frac{\sigma}{n}}_{p + " + (LaTeX[faktorWurzelN]) + " \cdot \frac{1}{\sqrt{n}}}"
Text3: "n = " + n + ""
Text6: "p = " + p + ""
Text2: "\text{\textcolor[rgb]{0,0.39,0}{" + (LaTeX[Prozentangabe]) + "}-\textcolor{blue}{Prognoseintervall\ für\ die\ absolute\ Trefferhäufigkeit\ X:}}\\ \mu - " + (LaTeX[faktorSigma]) + "\sigma =\textcolor{blue}{ " + (LaTeX[prognoseAbsLinks]) + "\leq X \leq " + (LaTeX[prognoseAbsRechts]) + "} = \mu + " + (LaTeX[faktorSigma]) + "\sigma "