Probability Laboratory

Formalism of ( Ω, F, P )

Sample Space (Ω)

The Ω is the set of all possible outcomes. In our mathematical framework, it must be clearly defined before we can build any event structures.

Axioms of Sigma-algebra (F)

A family of subsets F is a σ-algebra on Ω if it satisfies the following properties:

I. Non-emptiness

Ω ∈ F

The whole space is a measurable event.

II. Complement

A ∈ F ⇒ Ac ∈ F

If an event can occur, its non-occurrence is also measurable.

III. Countable Union

∪ Ai ∈ F

The union of any countable sequence of events is measurable.

Define Event A

Axioms of Measure (P)

P(A) ≥ 0 (Non-negativity)

P(Ω) = 1 (Normalization)

P(∪ Ai) = Σ P(Ai) (Countable Additivity)

Probability Measure

0.00