Random variable: Difference between revisions

Revision as of 05:44, 25 April 2002

Revision as of 05:52, 25 April 2002

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=== Moments ===

A random variable canis often be characterised by a small number of quantities, which also have a practical interpretation. For example, it is often enough to know what its "average value" is. This is captured by the mathematical concept of [[expected value]] of a random variable, denoted E[''X'']. Once the "average value" is known, one could then ask "how far arefrom the average value the values of ''X'' typically away from the average"are, a question that is answered by the [[variance]] and [[standard deviation]] of a random variable.

Mathematically, this is known as the (generalised) [[problem of moments]]: for a given class of random variables ''X'', find a collection {''f_i''} of functions such that the expectation values E[''f_i''(''X'')] fully characterize the distribution of the random variable ''X''.