Probability

Random variable: a quantity whose outcomes (possible values) are uncertain. (eg. return on a risky asset)

An event is a specified set of outcomes.

Probability:

1 The probability of any event E is a number between 0 and 1: 0 ≤ P(E) ≤ 1.

2 The sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1.

Mutually exclusive means that only one event can occur at a time; exhaustive means that the events cover all possible outcomes.

Objective probability: Empirical and Priori

Empirical probability estimates the probability of an event as a relative frequency of occurrence based on historical data. Relationships must be stable through time for empirical probabilities to be accurate.

Priori probability: deduce probabilities by reasoning about the problem. based on logical analysis rather than on observation or personal judgment.

Subjective probability draws on personal or subjective judgment.