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Summary

Summary For The Course Introduction Data Analysis, Tilburg University (UVT) - 1st Year - 1st Semester

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A summary for the textbook Statistical Methods for Business and Economics, ISBN: 9780077109875, for Inleiding Data-Analyse (350818-B-6). This can also be used for Introduction Data-Analysis. This is a summary that contains all formulas that are prescribed according to the syllabus of Inleiding D...

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Formuleblad Inleiding Data-Analyse | T1 & T2-Stof

Properties van een Verdeling:

A ∩ ( B∪ C )= ( A ∩ B ) ∪( A ∩ B)
A ∪ ( B ∩C )= ( A ∪ B ) ∩( A ∪ B) Regels voor Tellen:

( A ∩ B )C = A C ∪ B C m: Mogelijkheden

k: Aantal ‘Plaatsen’
( A ∪ B )C = AC ∩ B C
Geordend MET Terugleggen:
A ∪ A C =Ω
mk
A ∩ AC =∅(alsdisjunct )
Geordend ZONDER Terugleggen:
( A ∩ B ) ∪ ( A ∩ BC ) = A
m!
Klassieke Kansdefinitie: ( m−k ) !
N (A) ‘m’ nPr ‘k’ op rekenmachine
P ( A )=
N
Ongeordend ZONDER Terugleggen:
Classic Properties:
m!
= m = m boven k
()
 0 ≤ P(A) ≤ 1 k ! ( m−k ) ! k
 P(∅) = 0
 P ( A ∪ B ) =P ( A )+ P ( B ) ( alsdisjunct ) ‘m’ nCr ‘k’ op rekenmachine

Empirische Kansdefinitie: Binomiale Coëfficienten:


P ( A )=
n(A)
n
o (m0 )=1
Empirische Properties:

 0 ≤ P(A) ≤ 1
o (mm )=1
 P(∅) = 0 m =m
 P ( A ∪ B ) =P ( A )+ P ( B ) ( alsdisjunct ) o (m−1 )
General Definition of Kolmogorov:

 P(A) ≥ 0
o (mk )=( m−k
m
)
 P(Ω) = 1
 P ( A ∪ B ) =P ( A )+ P ( B ) ( alsdisjunct ) Conditional Probabilities & Dependence:

P ( A ∩ B)
Properties van een Partition: P ( A|B )=PB ( A )= note : P ( B )> 0
P (B )
C
 P ( A ) =1−P ( A )
P(A∩B)
 P ( ∅ ) =0 P ( B| A )=P A ( B )= note: P ( A ) >0
P( A )
 A ⊂B ⇒ P ( A )≤ P ( B)
S
Productregels:
 P ( A )= ∑ P ( A ∩ D i )
i=1
P ( A ∩B )=P ( A ) ⋅ P ( B| A )=P ( B ) ⋅P ( A| B )
 P ( A ∪ B ) =P ( A )+ P ( B )−P ( A ∩ B )
P ( A ∩B ∩C )=P ( A ) ⋅ P ( B| A ) ⋅ P ( C∨A ∩ B )

Independence If:

 P ( A|B )=P ( A )

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