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 )
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 )
