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Wahrscheinlichkeitserzeugende Funktionen. Ein analytischer Ansatz für stochastische Fragestellungen by Hirshman, Markus

Wahrscheinlichkeitserzeugende Funktionen. Ein analytischer Ansatz für stochastische Fragestellungen

by Markus Hirshman
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Book cover type: Paperback
  • ISBN13: 9783656837329
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 56
  • Original Price: USD 39.5
  • Language: German
  • Edition: N/A
  • Item Weight: 87 grams
  • BISAC Subject(s): Probability & Statistics / General

Studienarbeit aus dem Jahr 2014 im Fachbereich Mathematik - Stochastik, Rheinisch-Westfälische Technische Hochschule Aachen (Institut für Statistik und Wirtschaftsmathematik), Veranstaltung: Stochastik für Lehramtsstudierende, Sprache: Deutsch, Abstract: Mit Hilfe von wahrscheinlichkeitserzeugenden Funktionen können Fragen und Probleme aus dem Bereich diskreter Zufallsvariablen (genauer: Zufallsvariablen die als Träger die natürlichen Zahlen einschlie lich der 0 haben) in die Analysis verortet werden. Die wahrscheinlichkeitserzeugende Funktion einer solchen Zufallsvariablen ist dann als Potenzreihe gegeben. Neben einer einfachen Möglichkeit die üblichen Kenngrö en (Erwartungswert, Varianz und andere Momente) einer Zufallsvariablen zu berechnen, sind wahrscheinlichkeitserzeugende Funktionen vor allem in Anwendungsaufgaben von Bedeutung in denen man die genaue Verteilung der betrachteten Zufallsvariable nicht oder nur mit sehr gro em Aufwand angeben kann. Die wahrscheinlichkeitserzeugende Funktion liefert auch in solchen Fällen Kenngrö en und sogar konkrete Wahrscheinlichkeiten. Als Voraussetzung sind lediglich Grundkenntnisse der Analysis zum Umgang mit Reihen bzw. Potenzreihen und Grundkenntnisse der Stochastik notwendig, wie sie üblicherweise in einer Einführungsveran staltung gelehrt werden.

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