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Samenvatting Overzicht van statistiek

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Belangrijkste aspecten van statistiek in een overzichtelijke tabel gegoten. Kansrekenen, frequentietabellen, spreidingsmaten, populatie, steekproef, BI, regressie, associatie...

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  • January 17, 2023
  • 29
  • 2021/2022
  • Summary

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By: pomareslem • 3 weeks ago

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I. KANSREKENEN
SYMBOLEN Ω = uitkomsten verzameling = { 1,2,3,4,5,6 } = universum
𝐴 = 𝑔𝑒𝑏𝑒𝑢𝑟𝑡𝑒𝑛𝑖𝑠
𝑃(𝐴) = 𝑑𝑒 𝑘𝑎𝑛𝑠 𝑑𝑎𝑡 𝑔𝑒𝑏𝑒𝑢𝑟𝑡𝑒𝑛𝑖𝑠 𝐴 𝑧𝑖𝑐ℎ 𝑣𝑜𝑜𝑟𝑑𝑜𝑒𝑡
𝑃 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦


SCHEMA OPLOSSEN
volgens kansregel Laplace




Gebeurtenissen Samengestelde gebeurtenis = “2 of meer gooien”

Elementaire gebeurtenis = “1 gooien”

Zekere gebeurtenis = steeds minder dan 7 gooien

Onmogelijke gebeurtenis = 7 gooien

Kansregel van Laplace Als het universum Ω eindig is en als alle uitkomsten even waarschijnlijk
zijn, dan is
𝑎𝑎𝑛𝑡𝑎𝑙 𝑔𝑢𝑛𝑠𝑡𝑖𝑔𝑒 𝑢𝑖𝑡𝑘𝑜𝑚𝑠𝑡𝑒𝑛
𝑃(𝐴) = 𝑎𝑎𝑛𝑡𝑎𝑙 𝑚𝑜𝑔𝑒𝑙𝑖𝑗𝑘𝑒 𝑢𝑖𝑡𝑘𝑜𝑚𝑠𝑡𝑒𝑛
#𝐴
= #Ω
voor elke gebeurtenis 𝐴 ⊆ Ω


Lukraak = om aan te duiden dat alle uitkomsten even waarschijnlijk zijn


Relatieve frequentie Als het universum niet eindig is of niet alle uitkomsten zijn even
waarschijnlijk
→ mag de regel van Laplace NIET gebruikt worden

𝑎𝑎𝑛𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑒𝑛 𝑤𝑎𝑎𝑟𝑖𝑛 𝐴 𝑜𝑝𝑑𝑢𝑖𝑘𝑡
𝐷𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑒𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 = 𝑎𝑎𝑛𝑡𝑎𝑙 ℎ𝑒𝑟ℎ𝑎𝑙𝑖𝑛𝑔𝑒𝑛 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡

, KANSEN VAN GECOMBINEERDE GEBEURTENISSEN + venndiagram
Kans van de UNIE

A of B




Kans van het COMPLEMENT

Niet a




VOORWAARDElijke kansen

A als B




Kans van de DOORSNEDE

A en B




Kansregel van Laplace
A

, KANSBOMEN

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