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Zusammenfassung Deskriptive Statistik

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Deskriptive Statistik

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  • November 21, 2022
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19. Statistik

BINOMIALVERTEILUNG

WIEDERHOLUNG: WÜRFELWURF UND WAHRSCHEINLICHKEITEN

z.B. Die Wahrscheinlichkeit, eine 6 zu
würfeln ist 16.6 Prozent.

Bei unendlichem Würfeln tritt die 6 in
16.6 Prozent der Würfe auf



N=1000 N=10000 N=100000

Bernoulli Theorem: „Die Wahrscheinlichkeit entspricht der relativen Häufigkeit bei unendlichen Wiederholungen
eines Zufallsexperiments.“



WIEDERHOLUNG: WÜRFELWURF UND WAHRSCHEINLICHKEITEN

ZUFALLSEXPERIMENT

mehrere Stichproben gleichen Umfangs werden gezogen:

Die Anteile der Würfe „6“ variieren um 16.6 Prozent

ERWEITERUNG AUF 1000 STICHPROBEN MIT JE 100 WÜRFEN



BINOMIALVERTEILUNG

Die Wahrscheinlichkeitsverteilung nennt man Binomialverteilung.

Der Ausdruck



hängt nur von 𝑛 und 𝑝 ab.

Man nennt die Zufallsvariable 𝑋 daher 𝑩𝒏;𝒑-verteilt.



EIGENSCHAFTEN EINER BINOMIALVERTEILUNG

E (x) ist der Wert, der bei unendlich vielen Wiederholungen des Experiments im Durchschnitt für jede Stichprobe zu
erwarten ist.

Var (x) sagt aus, wie stark die Werte um den Erwartungswert schwanken.

Erwartungswert: E(X) = n ∙ p

Varianz: VAR(X) = n ∙ p ∙ (1-p)

Standardabweichung: STD(X) = n ∙ p ∙ (1−p)



Beispiel des Würfels: E (x) = n * p = 100*0,1666 = 16,6

Var (x) = n * p * (1-p) = 100*0,1666 * 0,8333= 13,8

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