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Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
For independent random variables X and Y, the distribution f Z of Z = X + Y equals the convolution of f X and f Y: = ()Given that f X and f Y are normal densities, = (;,) = / () = (;,) = / ()
We use the term fringe theory in a very broad sense to describe an idea that departs significantly from the prevailing views or mainstream views in its particular field. For example, fringe theories in science depart significantly from mainstream science and have little or no scientific support. [3]
The term "multiple independent sources" in journalism, criminal justice, science [1] and general research, [2] [3] refers to two or more unconnected people, organizations, entities or objects which provide a given set of information or samples.
Assumptions vs. inferences: In uncertainty and sensitivity analysis there is a crucial trade off between how scrupulous an analyst is in exploring the input assumptions and how wide the resulting inference may be. The point is well illustrated by the econometrician Edward E. Leamer: [58] [59]
This page in a nutshell: Independent sources are distinguished by their lack of any direct influence with the subjects involved. Wikipedia encourages the use of independent sources because these sources are typically associated with reliability, a lack of bias, and factual accuracy.