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Bevis av centrala gränsvärdessatsen med hjälp av Lévys sats
Örebro University, School of Science and Technology.
2017 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Proving the Central Limit Theorem Using Lévy’s Continuity Theorem (English)
Abstract [sv]

Centrala gränsvärdessatsen (CGS) är en av grundpelarna inom statistik

och sannolikhetsteori. CGS säger att ”summan av ett stort antal oberoende

likafördelade slumpmässiga variabler är approximativt normalfördelad”. Det

finns olika bevis för CGS. I denna uppsats kommer jag att bevisa centrala

gränsvärdessatsen genom att utnyttja karaktäristiska funktioner, eftersom

karaktäristiska funktioner har bra egenskaper vilket vi kommer att få se när

vi definierar dem. I detta arbete har jag kopplat samman olika pusselbitar

som behövs för att kunna bevisa CGS. Genom att göra det så blir det enklare

för läsaren att förstå CGS mer grundläggande.

Abstract [en]

The Central Limit Theorem (CLT) is one of the pillars of statistics and probability

theory. CLT states that ”the sum of a large number of independent

equally distributed random variables is approximately normally distributed”.

There are different proofs for CLT. In this essay I will prove the central limit

theorem by utilizing characteristic functions, since characteristic functions

have good features, which we will see when defining them. In this paper I

have linked various pieces of the puzzle needed to prove CLT. By doing so it

becomes easier for readers to gain a deeper understanding of CLT.

Place, publisher, year, edition, pages
2017. , p. 21
Keywords [sv]
CGS, normalfördelning, stokastisk, oberoende
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-58389OAI: oai:DiVA.org:oru-58389DiVA, id: diva2:1117859
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2017-10-18Bibliographically approved

Open Access in DiVA

fulltext(542 kB)53 downloads
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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