Flashcards
Chapter 1: Basic Probability Theory
Flashcards do conjunto (5)
- 1What are the 3 properties of a sigma field?1. contains a null empty set
\[ \emptyset \in \mathcal{F} \]
2. closed under unions
3. closed under compliments
\[ if A \in \mathcal{F} \] then \[A^c \in \mathcal{F} \] - 2What are the 3 elements of a probability space?\( (\Omega\ , \mathcal{F} , P) \)
\(\sigma\) - field
\(\Omega\) - Set of outcomes
P - probability Measure - 3What is the range of the probability measure?between 0 and 1
P(null set) = 0, P(solution set) = 1 - 4What is the Identity of the probability measure?Given disjoint events, the probability of the union of events \(A_n\) = sum of individual probabilities of events \(A_n\)
\[ P \big( \bigcup\limits_{i=1}^{\infty} A_i \big) = \sum \limits_{i=1}^{\infty} P(A_i) \] - 5What is the equation of A conditional on B?\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \]
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- Descrição
- Probability FlashCards sobre Chapter 1: Basic Probability Theory, criado por Lewis Warne em 28-05-2018.
- Criado por
- Lewis Warne
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