lecture outline
- Probability as a mathematical framework for resoning about uncertainty
- Probabilistic models(sample space, probability law)
- Axioms of probability
Sample spaceOmega
- "list" (set) of possible outcomes
- list (Mutually exclusive, Collectively exhaustive)
- Art: to be at the "right" granularity
- Discrete example
- Continuous example
Probability axioms
- Event : a subset of the sample space
- Probability is assigned to events
Discrete uniform law
- P(A) = number of elements of A / total number of sample points
- Computing probabilities == counting
Continuous uniform law
- Uniform law: probability = Area
Probability law
- if A1, A2, ... are disjoint events, then:
P(A1 and A2 and ... ) = P(A1) + P(A2) + ...
