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Bevis av centrala gränsvärdessatsen: med hjälp av Levys sats
Örebro University, School of Science and Technology.
2018 (Swedish)Independent thesis Basic level (professional degree), 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 definerar 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
2018. , p. 21
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-71059OAI: oai:DiVA.org:oru-71059DiVA, id: diva2:1274204
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2018-12-28 Created: 2018-12-28 Last updated: 2018-12-28Bibliographically approved

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Bevis av centrala gränsvärdessatsen(542 kB)10 downloads
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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf