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Exponentialverteilung - Mathematik mit Software by Kramer, Bianca

Exponentialverteilung - Mathematik mit Software

by Bianca Kramer
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Book cover type: Paperback
  • ISBN13: 9783656339601
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 40
  • Original Price: GBP 30.9
  • Language: German
  • Edition: N/A
  • Item Weight: 64 grams
  • BISAC Subject(s): Probability & Statistics / General

Studienarbeit aus dem Jahr 2010 im Fachbereich Mathematik - Stochastik, Note: 1,0, Universität Kassel, Veranstaltung: Mathematik mit Software, Sprache: Deutsch, Abstract: Eine Wahrscheinlichkeitsverteilung ist ein mathematisches Mittel zur Beschreibung von Zufallsprozessen. Die Wahrscheinlichkeitsverteilung einer Zufallsgrö e ist eine Funktion, die jedem Wert einer Zufallsgrö e X eine Wahrscheinlichkeit zuordnet. Die Wahrscheinlichkeitsverteilung w einer Zufallsgrö e X ist demnach auf der Wertemenge der Zufallsgrö e X definiert. Mithilfe einer Tabelle oder einem Grafen, wie z. B. einem Histogramm, kann man die Verteilung einer Zufallsgrö e angeben. Auch die Exponentialverteilung ist eine Wahrscheinlichkeitsverteilung über der Menge der positiven reellen Zahlen. Der Graf der Exponentialverteilung ist in der Form einer Exponentialfunktion gegeben. Das Modell der Exponentialverteilung wird vorrangig für die Darstellung von zufälligen Zeitintervallen benutzt. Bekannte Sachverhalte dafür sind Lebensdauern, wie z. B. die Lebensdauer von Atomen beim radioaktiven Zerfall, die Lebensdauer von Bauteilen, Maschinen und Geräten oder auch die Zeit zwischen zwei Telefonanrufen. Die Exponentialverteilung ist also eine typische Lebensdauerverteilung, da die Lebensdauer von elektronischen Bauteilen meistens annähernd exponentialverteilt ist. Oft ist die tätsächliche Verteilung nicht exakt eine Exponentialverteilung, sie wird aber zur Vereinfachung unterstellt. Im ersten Kapitel dieser Arbeit werden zunächst die Definition der Exponentialverteilung präsentiert und im Folgenden die wichtigsten Eigenschaften dargelegt und erklärt. Besonders hervorgehoben wird dabei der Erwartungswert der Exponentialverteilung, indem dessen ausführliche Herleitung erfolgt. Im zweiten Kapitel wird das Verhältnis zur geometrischen Verteilung erklärt und mithilfe von Fathom untersucht. Im dritten Kapitel werden Aufgaben um exponentialverteilte Zufallsgrö en theoretisch gelöst und diese Lösung dann mit

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