Algebra of Random Variables
Alternate name
Definition
Given an event E in a sample space S which is either finite with N elements or countably infinite with N = ∞ elements, then we can write S congruent ( union _(i = 1)^N E_i), and a quantity P(E_i), called the probability of event E_i, is defined such that 1.0<=P(E_i)<=1. 2.P(S) = 1. 3. Additivity: P(E_1 union E_2) = P(E_1) + P(E_2), where E_1 and E_2 are mutually exclusive. 4. Countable additivity: P( union _(i = 1)^n E_i) = sum_(i = 1)^n P(E_i) for n = 1, 2, ..., N where E_1, E_2, ... are mutually exclusive (i.e., E_1 intersection E_2 = ∅).
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