Vorlesungen ber Wahrscheinlichkeitstheorie (Teubner Studienbcher Mathematik) (German Edition),New

Vorlesungen ber Wahrscheinlichkeitstheorie (Teubner Studienbcher Mathematik) (German Edition),New

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Den Titel 'Vorlesungen liber Wahrscheinlichkeitstheorie' habe ich sehr bewuBt gewahlt. Einerseits will und soll dieses Buch seine Entstehung aus Kursvorlesungen flir MathematikStudenten nicht verleugnen. Der tiefere Grund liegt jedoch in der Zielsetzung und in der daraus re sultierenden Art der Darstellung: Ich machte erreichen, daB der Leser wichtige Intentionen, grundlegende Ideen und interessante Aussagen der Wahrscheinlichkeitstheorie versteht sei es im Selbststudium oder sei es in Erganzung zu Lehrveranstaltungen. Daraufhin nehmen die Mo tivationen der Begriffsbildungen, die Erlauterungen der Aussagen und die illustrationen durch Beispiele wie sie ein Dozent liber die reine Stoffprasentation hinaus seinen Harern in VOrlesungen vermittelt einen erheblich breiteren Raum ein als liblich. Hieraus ergibt sich andererseits, daB es mir nicht urn maglichste Allgemeinheit der Aussagen oder 'tech nisch' aufwendige Zusatzliberlegungen geht. Trotz dieser Einschrankun gen hoffe ich aber, daB Studierende hiermit liber eine Basis verfligen, urn sich einerseits anspruchsvollere Lehrblicher und Originalliteratur er arbeiten zu kannen, urn andererseits einen Zugang zu spezielleren Teil gebieten der Wahrscheinlichkeitstheorie (z. B. Zeitreihenanalyse, Geburts und Todesprozesse/Warteschlangentheorie, Erneuerungstheorie, Verzwei gungsprozesse, Zuverlassigkeitstheorie, Markoffsche Entscheidungsprozesse, Informationstheorie) zu finden und urn schlieBlich die Denk und SchluBweisen der Mathematischen Statistik verstehen zu kannen. Aufgabe der Wahrscheinlichkeitstheorie ist es, mathematische Modelle flir zufallsabhangige Vorgange zu entwickeln und im Rahmen dieser abstrakten Modelle zu Aussagen zu gelangpn, die bei ihrer Rlicklibersetzung in die Re alitat GesetzmaBigkeiten sichtbar werden lassen und so als Grundlagen flir rationale Entscheidungen dienen kannen. Im ersten Teil dieses Lehrbuchs (14) wird besonderes Gewicht auf die Modellbildung gelegt.

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