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4. Bedingte Wahrscheinlichkeit

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Author
Andrea Pascucci
Published in
Elementare Wahrscheinlichkeitstheorie I
Publisher
Springer Nature Switzerland

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Zusammenfassung

In einem Wahrscheinlichkeitsraum \(({\Omega },\mathscr {F},P)\), sei X eine Zufallsvariable und \(\mathscr {G}\) eine Unter-\({\sigma }\)-Algebra von \(\mathscr {F}\). In diesem Kapitel führen wir die Konzepte der bedingten Verteilung und Erwartung von X gegeben \(\mathscr {G}\) ein. In Erinnerung daran, dass eine \({\sigma }\)-Algebra als eine Menge von „Informationen“ interpretiert werden kann, repräsentiert die bedingte Erwartung von X gegeben \(\mathscr {G}\) die beste Schätzung des Zufallswertes X basierend auf den Informationen enthalten in \(\mathscr {G}\).
Wir haben es nicht geschafft, alle unsere Probleme zu beantworten – tatsächlich haben wir manchmal das Gefühl, dass wir keines von ihnen vollständig beantwortet haben. Die Antworten, die wir gefunden haben, haben nur dazu gedient, eine ganze Reihe neuer Fragen aufzuwerfen. In gewisser Weise haben wir das Gefühl, dass wir immer noch genauso verwirrt sind wie zuvor, aber wir glauben, dass wir auf einer höheren Ebene und über wichtigere Dinge verwirrt sind.
.
Earl C. Kelley

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previous chapter Folgen von Zufallsvariablen
next chapter Zusammenfassende Übungen
Title
Bedingte Wahrscheinlichkeit
Author
Andrea Pascucci
Copyright Year
2025
Book
Elementare Wahrscheinlichkeitstheorie I

Print ISBN: 978-3-031-98092-3

Electronic ISBN: 978-3-031-98093-0

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-98093-0_4
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