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Probability (formal definition)

The value P(A) of an event A under a probability distribution P.

Certain event (P(Ω)=1)

Term for the entire sample space Ω viewed as event.

Impossible event (P(∅)=0)

Term for the empty set ∅ viewed as event.

Complementary event

The event with probability 1–P(A) that a given event A does not occur.

(Discrete) Random variable

A map X from Ω to the real or complex numbers (or sometimes any set) for a given discrete probability space (Ω,P).

(Discrete) Multivariate random variable

A vector-valued map X : Ω → R^n for a given discrete probability space (Ω,P).

(Discrete) Random element

A map X : Ω → E for a given discrete probability space (Ω,P) to an arbitrary set E (emphasizing that X is not real-valued).

Independent events

Two events A, B that satisfy P(A ∩ B) = P(A)P(B).

Independent and identically distributed

The common property of a family of random variables that is abbreviated by "i.i.d.".

Partition (of a set)

Division of a set S into non-overlapping (mutually exclusive) and non-empty subsets that cover all of X (collectively exhaustive).