Probability
Sample space
- Describe possible outcome
- Describe beliefs about likelihood of outcome
Probability Law
Axioms
Properties that follows from axioms
type of probabilities
Discrete probability
Continuous probability
Discussion about
Countable activity
Mathematical Subtleties
Interpretation of Probability
- Description of beliefs
- Betting Preference
A better definition - Rules of consistent reasoning
- used for predictions and decision
definition- Set of the possible outcome
List must be
- Mutually exclusive
- collectively exhaustive
- At the right granularity
Event - a subset of the sample space
- Probability is assigned to the Event
Axioms - Non-negativity
- Normalization
- (Finite) Additivity
Probability Calculation steps
- Specify the Sample space
- Specify a probability Law
- Identify the event of interest
- Calculate ..
Examples
Discrete Sample space
- tetrahedra cube
Continuous Probability Space
- Throwing Dart
Countable additivity
- Discrete but infinite sample space
- an infinite sequence of disjoint events
- Additivity holds only for countable sequences of event
The unit square is not countable
(its events cannot be arranged into a sequence )