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Leeroverzicht - Statistische Methoden (STM, 4052STAME) - MST $4.85
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Leeroverzicht - Statistische Methoden (STM, 4052STAME) - MST
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  • Course
  • Statistische Methoden (4052STAME)
  • Institution
  • Technische Universiteit Delft (TU Delft)
  • Book
  • A Modern Introduction to Probability and Statistics

Het vak Statische Methoden behandelt een aantal basisprincipes van de kansrekening en statistiek en de statistische denkwijze. Het vak wordt gegeven in de eerste periode van het tweede jaar van de opleiding Molecular Science & Technology aan de Universiteit Leiden en de TU Delft. In dit document z...

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  • October 28, 2020
  • 6
  • 2020/2021
  • Study guide

Subjects

  • statistische
  • methoden
  • leeroverzicht
  • formuleblad
  • mst
  • molecular
  • science
  • technology
  • stm
  • 4052stame
  • stame

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  • Technische Universiteit Delft (TU Delft)
  • Molecular Science and Technology
  • Statistische Methoden (4052STAME)
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4052STAME LEEROVERZICHT




Statistische methoden
4052STAME

Leeroverzicht




Pagina 1 van 6

, 4052STAME LEEROVERZICHT

Kansrekening
Rekenen met kansen
Somregel: P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) = P ( A ) + P B ∩ A c ( )
P ( A ∪ B ∪ C ) = P ( A ) + P ( B ) + P (C ) − P ( A ∩ B ) − P ( A ∩ C ) − P ( B ∩ C ) + P ( A ∩ B ∩ C )
( )
Complementregel: P A c = 1− P ( A )

P ( A | B ) = 1− P ( A | B )
c



( A ∪ B )C = AC ∩ BC
Regel van deMorgan:
( A ∩ B )C = AC ∪ BC
P(A ∩ C)
Conditionele kans: P ( A | C ) = mits P ( C ) > 0 .
P (C )
Vermenigvuldigheidsregel: P ( A ∩ C ) = P ( A | C ) P ( C ) = P ( C | A ) P ( A ) .
Regel voor de totale kans: P ( A ) = P ( A | C1 ) P ( C1 ) + P ( A | C2 ) P ( C2 ) + ...+ P ( A | Cm ) P ( Cm )
P ( A ) = P ( A | C ) P (C ) + P ( A | C C ) P (C C )
P ( A | B) P ( B)
Bayes Rule: P ( B | A ) =
P ( A)
P ( A | Ci ) P ( Ci )
P ( Ci | A ) =
P ( A | C1 ) P ( C1 ) + ...+ P ( A | Cm ) ( Cm )

Onafhankelijkheid
P ( A | B) = P ( A)
P ( B | A) = P ( B)
P ( A ∩ B) = P ( A) P ( B)
P ( A1 ∩ A2 ∩ ...∩ Am ) = P ( A1 ) P ( A2 ) ...P ( Am )

Verwachtingswaarde
Discreet: E [ X ] = ∑a • P( X = a ) .
i i
ai
∞ ∞
Continu: E [ X ] = ∫ xf ( x ) dx , E ⎡⎣ X 2 ⎤⎦ = ∫ x 2 f ( x ) dx , E ⎡⎣ X 2 ⎤⎦ = Var ( X ) + E [ X ]
2
−∞ −∞


Variantie
Var ( X ) = E ⎡⎣ X 2 ⎤⎦ − ( E [ X ])
2



Var ( X + Y ) = E ⎡⎣( X + Y ) ⎤⎦ − ( E [ X + Y ])
2 2




Jensens ongelijkheid
g ( E [ X ]) < E ⎡⎣ g ( X ) ⎤⎦ g'' ( x ) > 0 Convexe functies

g ( E [ X ]) = E ⎡⎣ g ( X ) ⎤⎦ g'' ( x ) = 0 Lineaire functies, deze zijn convex en concaaf tegelijkertijd

g ( E [ X ]) > E ⎡⎣ g ( X ) ⎤⎦ g'' ( x ) < 0 Concave functies



Pagina 2 van 6

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