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If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.

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 ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...

A principle that was first enunciated by Jakob Bernoulli which states that if we are ignorant of the ways an event can occur (and therefore have no reason to believe that one ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

Define T as the set of all points t with probabilities P(x) such that a>t=>P(a<=x<=a+da)<P_0 or a<t=>P(a<=x<=a+da)<P_0, where P_0 is a point probability (often, the ...

Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a ...

Given an event E in a sample space S which is either finite with N elements or countably infinite with N=infty elements, then we can write S=( union _(i=1)^NE_i), and a ...

An experiment E(S,F,P) is defined (Papoulis 1984, p. 30) as a mathematical object consisting of the following elements. 1. A set S (the probability space) of elements. 2. A ...