Probability
Probability is the branch of mathematics which studies the possible outcomes of given events together with their relativelikelihoods and distributions. In common usage, the word ``probability'' is used to mean the chance that a particular event(or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as aPercentage between 0 and 100%. The analysis of events governed by probability is called Statistics.
There are several competing interpretations of the actual ``meaning'' of probabilities. Frequentists view probability simplyas a measure of the frequency of outcomes (the more conventional interpretation), while Bayesianstreat probability more subjectively as a statistical procedure which endeavors to estimate parameters of an underlyingdistribution based on the observed distribution.
A properly normalized function which assigns a probability ``density'' to each possible outcome within some interval is calleda Probability Function, and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a Distribution Function.
Probabilities are defined to obey certain assumptions, called the Probability Axioms. Let a Sample Space containthe Union (
) of all possible events 
, so
 | (1) |
and 
denote subsets of 
. Further, let 
be the complement of , so that | (2) |
can be written as | (3) |
denotes the intersection. Then |  |  | |
|  | ||
|  | ||
|  | ||
|  | (4) |
where
is the Empty Set.Let 
denote the Conditional Probability of given that has already occurred, then
| |  | (5) |
|  | (6) | |
 | |  | (7) |
|  | (8) | |
 | |  | (9) |
 | |  | (10) |
A very important result states that
 | (11) |
 | |
 | |
| (12) |
- Fuhrmann's Theorem
- Fuhrmann Triangle
- Fuller Dome
- Full Reptend Prime
- Full Width at Half Maximum
- Function
- Functional
- Functional Analysis
- Functional Calculus
- Functional Derivative
- Function Field
- Function Space
- Functor
- Fundamental Class
- Fundamental Continuity Theorem
- Fundamental Discriminant
- Fundamental Forms
- Fundamental Group
- Fundamental Homology Class
- Fundamental Lemma of Calculus of Variations
- Fundamental System
- Fundamental Theorem of Algebra
- Fundamental Theorem of Arithmetic
- Fundamental Theorem of Curves
- Fundamental Theorem of Directly Similar Figures