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Mathematically, this is known as the (generalised) [[problem of moments]]: for a given class of random variables ''X'', find a collection {''f<sub>i</sub>''} of functions such that the expectation values E[''f<sub>i</sub>''(''X'')] fully characterize the distribution of the random variable ''X''.
=== Convergence ===
Much of mathematical statistics consists in proving convergence results for certain [[sequence]]s of random variables; see for instance the [[law of large numbers]] and the [[central limit theorem]].
There are various senses in which a sequence (''X''<sub>''n''</sub>) of random variables can converge to a random variable ''X''. These are explained in the article on [[convergence of random variables]].
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See also: [[discrete random variable]], [[continuous random variable]], [[probability distribution]], [[randomness]], [[random vector]], [[random function]], [[generating function]]
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