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Independence is a condition of a nation, country, or state, in which residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the status of a dependent territory or colony.
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.
The definition extends naturally to more than two random variables. We say that n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} are i.i.d. if they are independent (see further Independence (probability theory) § More than two random variables ) and identically distributed, i.e. if and only if
A set of rules governing statements of conditional independence have been derived from the basic definition. [4] [5] These rules were termed "Graphoid Axioms" by Pearl and Paz, [6] because they hold in graphs, where is interpreted to mean: "All paths from X to A are intercepted by the set B". [7]
The meaning of the Declaration was a recurring topic in the famed debates between Lincoln and Stephen Douglas in 1858. Douglas argued that the phrase "all men are created equal", which appears in the Declaration. referred to white men only.
An 1825 invitation to an Independence Day celebration A 2014 Independence Day parade in Washington, D.C., the national capital Independence Day is a national holiday marked by patriotic displays. Per 5 U.S.C. § 6103 , Independence Day is a federal holiday, so all non-essential federal institutions (such as the postal service and federal courts ...
Dictionary.com has a more general definition: “Gyatt or gyat is a slang term that is used to express strong excitement, surprise, or admiration.” Brush up on the latest teen slang
The linear dependency of a sequence of vectors does not depend of the order of the terms in the sequence. This allows defining linear independence for a finite set of vectors: A finite set of vectors is linearly independent if the sequence obtained by ordering them is linearly independent. In other words, one has the following result that is ...