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) + ...

Topic of probabilities