Summary: Samenvatting Statistiek Tisem Athena (2) Kopie

Read the summary and the most important questions on Samenvatting Statistiek TiSEM Athena (2) kopie

• 1 1.1 Definitions

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• What is an EVENT in probability?

  An event is a subset of Ω with possible outcomes.
  

  • Represents one or more outcomes
  • Notation: empty set is ∅
  • Example events can vary in size

• How do we denote the INTERSECTION of two events?

  The intersection is denoted by A ∩ B.
  

  • Represents A and B together
  • Only common outcomes considered
  • Example: A = {2, 3}, B = {3, 4} yields {3}

• What does the COMPLEMENT of an event signify?

  The complement includes all outcomes not in A.
  

  • Denoted by A^c
  • Example: A = {2, 3} leads to A^c = {1, 4, 5, 6}
  • Opposite of event in question

• What is the first rule for sets involving UNION and COMPLEMENT?

  A ∪ A^c equals Ω.
  

  • Combines all elements from A and its complement
  • Total outcomes represented
  • Represents the entire sample space

• What does the third rule for sets state?

  A ∩ (B ∪ C) equals (A ∩ B) ∪ (A ∩ C).
  

  • Distributes intersections over unions
  • Shows relationship between operations
  • Ensures outcomes are accounted for

• What does the fourth rule for sets indicate?

  A ∪ (B ∩ C) equals (A ∪ B) ∩ (A ∪ C).
  

  • Distributes unions over intersections
  • Combines elements appropriately
  • Ensures accuracy of outcomes

• What is the fifth rule for sets' interaction with COMPLEMENT?

  (A ∪ B)^c equals A^c ∩ B^c.
  

  • Shows relationship of unions and complements
  • Indicates common non-included outcomes
  • Validates understanding of set operations

• What does the notation Ω represent in probability?

  Ω represents the sample space including all possible outcomes.
  

  • Denotes all results from an experiment
  • Example for six-sided die: Ω = {1, 2, 3, 4, 5, 6}
  • Fundamental concept in random experiments

• How is the empty set represented in set theory?

  The empty set is denoted by ∅.
  

  • Contains no elements
  • Represents no outcomes in an event
  • Important in defining events and subsets

• 7 6 Bayes’ Theorem :

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• What is the formula for P(B|A)?

  • P(B|A) =
  • P(A|B) × P(B)
  • / [ P(A|B) × P(B) + P(A|B c) × P(B c) ]