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Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of the classical notion of independence , and it is connected with free products .
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.
A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values [15] (almost surely) [16] which means that the probability of any event can be expressed as a (finite or countably infinite) sum: = (=), where is a countable set with () =.
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} , instead of the standard [ 0 , 1 ] {\displaystyle [0,1]} unit interval .
The classical definition of probability assigns equal probabilities to events based on physical symmetry which is natural for coins, cards and dice. Some mathematicians object that the definition is circular. [11] The probability for a "fair" coin is... A "fair" coin is defined by a probability of... The definition is very limited.