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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.
Independent: Each outcome will not affect the other outcome (for from 1 to 10), which means the variables , …, are independent of each other. Identically distributed : Regardless of whether the coin is fair (with a probability of 1/2 for heads) or biased, as long as the same coin is used for each flip, the probability of getting heads remains ...
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 New York Times's minimal standard for reporting a fact not otherwise attributed to a single speaker is that it be verified by at least two independent sources. Circular reporting is a situation where multiple sources appear to be independent, but in reality originate from a single source. Because circular reporting can happen inadvertently ...
It can be subdivided into source coding theory and channel coding theory. Using a statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source. Data compression (source coding): There are two formulations for the compression problem:
ICA finds the independent components (also called factors, latent variables or sources) by maximizing the statistical independence of the estimated components. We may choose one of many ways to define a proxy for independence, and this choice governs the form of the ICA algorithm. The two broadest definitions of independence for ICA are
If two independent events are measured separately, the total amount of information is the sum of the self-informations of the individual events. The detailed derivation is below, but it can be shown that there is a unique function of probability that meets these three axioms, up to a multiplicative scaling factor.
Shannon's definition of entropy, when applied to an information source, can determine the minimum channel capacity required to reliably transmit the source as encoded binary digits. Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable).