P(X>=k)

P(X<=k)

Ablehnungsbereich anzeigen

P(X=k)

Gegenereignis

Erwartungswert μ anzeigen

P(X∈[μ-c,μ+c])

k_k = 20 (slider from 0 to n, step 1)
k_{links} = 20 (slider from 0 to n, step 1)
n = 80 (slider from 0 to 200, step 1)
p = 0.25 (slider from 0 to 1, step 0.01)
q: 1 - p
k_{rechts} = 20 (slider from 0 to n, step 1)
a_{lr} = BarChart(k_{rechts} - 0.5, k_{links} + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, k_{rechts}, k_{links}])
binom: BinomialDist[n, p, k_{links}, true] - BinomialDist[n, p, k_{rechts} - 1, true]
b = BarChart(-0.5, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, n])
x_Achse: n + 2
y_Achse = 0.5
a_r = BarChart(k_{rechts} - 0.5, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, k_{rechts}, n])
a_l = BarChart(-0.5, k_{links} + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, k_{links}])
Anzeigen_r = false
Anzeigen_l = true
P_{Max} = BinomialDist(n, p, round((n * p)), false)
k_{max}: round((p * n))
binom_l = BinomialDist(n, p, k_{links}, true)
binom_r: 1 - BinomialDist[n, p, k_{rechts} - 1, true]
α = 0.05 (slider from 0 to 1, step 0.01)
signifikanzniveau: "Signifikanzniveau   \alpha=" + (LaTeX[α]) + ""
Liste_l = Sequence(BinomialDist[n, p, i, true], i, 0, n)
Liste_r = Sequence(1 - BinomialDist[n, p, i - 1, true], i, 0, n)
A_l = Sequence(Element[Liste_l, k]  <  α, k, 1, Length[Liste_l])
Index_l: IndexOf[false, A_l] - 2
Ablehnung_l = BarChart(-0.5, Index_l + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, Index_l])
A_r = Sequence(Element[Liste_r, k]  <  α, k, 1, Length[Liste_r])
Index_r: IndexOf[true, A_r] - 1
Ablehnung_r = BarChart(Index_r - 0.5, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, Index_r, n])
Ablehnung_an = false
TextP_{links}: "k=" + (LaTeX[k_{links}]) + "→P(X≤k)=P(X≤" + (LaTeX[k_{links}]) + ")=" + (LaTeX[a_l]) + ""
TextP_{rechts}: "k=" + (LaTeX[k_{rechts}]) + "→P(X≥k)=P(X≥" + (LaTeX[k_{rechts}]) + ")=" + (LaTeX[binom_r]) + ""
a_k = BarChart(k_k - 0.5, k_k + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, k_k, k_k])
Anzeigen_k = false
Laenge_n: "Länge der Bernoulli-Kette: n = " + n + ""
Text_P: "Trefferwahrscheinlichkeit: p=" + (LaTeX[p]) + ""
a_{lg} = BarChart(0.5 + k_{links}, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, k_{links} + 1, n])
Anzeigen_g = false
a_{kgr} = BarChart(0.5 + k_k, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, k_k + 1, n])
a_{kgl} = BarChart(-0.5, k_k - 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, k_k - 1])
a_{rg} = BarChart(-0.5, k_{rechts} - 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, k_{rechts} - 1])
Text_{kg}1: "P(\overline{X=k})=P(X≤" + (LaTeX[k_k - 1]) + ")+P(X≥" + (LaTeX[k_k + 1]) + ")"
Text_{kg}2: "=" + (LaTeX[a_{kgl} + a_{kgr}]) + ""
Text_{gr}: "P(\overline{X≥k})=P(X≤" + (LaTeX[k_{rechts} - 1]) + ")=" + (LaTeX[a_{rg}]) + ""
Text_{gl}: "P(\overline{X≤k})=P(X≥" + (LaTeX[k_{links} + 1]) + ")=" + (LaTeX[a_{lg}]) + ""
mue: (n * p)
Erwartungswert = Segment((mue, ((-P_{Max}) * 0.05)), (mue, 0))
TextP_k: "k=" + (LaTeX[k_k]) + "→P(X=k)=P(X=" + (LaTeX[k_k]) + ")= " + (LaTeX[a_k]) + " "
erwartungswerts2 = Segment((mue, P_{Max}), (mue, (P_{Max} * 1.05)))
EWert_1: "E(X)=μ = n·p=" + (LaTeX[n]) + "·" + (LaTeX[p]) + "= " + (LaTeX[(n * p)]) + ""
a = true
EVektor = Vector((mue, (0.2 * P_{Max})), (mue, 0))
c = 1 (slider from 0 to Min[n - mue, mue], step 1)
d = BinomialDist(n, p, mue - c, true)
a_{mue} = BarChart(mue - c - 0.5, mue + c + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, mue - c, mue + c])
Anzeigen_m = false
a_{mue}gl = BarChart(-0.5, mue - c - 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, 0, mue - c - 1])
a_{mue}gr2 = BarChart(mue + c + 0.5, n + 0.5, Sequence[((Binomial[n, k] * p^(k)) * q^(n - k)), k, mue + c + 1, n])
TextC: "c=" + (LaTeX[c]) + "→P(X∈[μ-c;μ+c])=P(X∈[" + (LaTeX[mue - c]) + ";" + (LaTeX[mue + c]) + "])=" + (LaTeX[a_{mue}]) + ""
TextC_{gmue}: "P(\overline{X∈[" + (LaTeX[mue - c]) + " ;" + (LaTeX[mue + c]) + " ]})
= P(X≤" + (LaTeX[mue - c - 1]) + ")+P(X≥" + (LaTeX[mue + c + 1]) + ")"
TextC2_{gmue}: "= P(X≤" + (LaTeX[mue - c - 1]) + " )+1-P(X≤" + (LaTeX[mue + c]) + " )"
TextC3_{gmue}: "=" + (LaTeX[a_{mue}gl]) + "+" + (LaTeX[a_{mue}gr2]) + "=" + (LaTeX[a_{mue}gl + a_{mue}gr2]) + ""