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Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...

A triple (S,S,P) on the domain S, where (S,S) is a measurable space, S are the measurable subsets of S, and P is a measure on S with P(S)=1.

If B superset A (B is a superset of A), then P(A)<=P(B).

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

alpha(x) = 1/(sqrt(2pi))int_(-x)^xe^(-t^2/2)dt (1) = sqrt(2/pi)int_0^xe^(-t^2/2)dt (2) = 2Phi(x) (3) = erf(x/(sqrt(2))), (4) where Phi(x) is the normal distribution function ...

Probability and Statistics

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

X fulfils the T1-separation axiom and is regular. A space satisfying the T_3-separation axiom is said to be a T3-space.