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Definitions II (Discrete)


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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).