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单词 RandomVariable
释义

random variable


If (Ω,𝒜,P) is a probability spaceMathworldPlanetmath, then a random variableMathworldPlanetmath on Ω is a measurable functionMathworldPlanetmath X:(Ω,𝒜)S to a measurable spaceMathworldPlanetmathPlanetmath S (frequently taken to be the real numbers with the standard measure). The law of a random variable is the probability measure PX-1:S defined by PX-1(s)=P(X-1(s)).

A random variable X is said to be discrete if the set {X(ω):ωΩ} (i.e. the range of X) is finite or countable. A more general version of this definition is as follows: A random variable X is discrete if there is a countable subset B of the range of X such that P(XB)=1 (Note that, as a countable subset of , B is measurable).

A random variable Y is said to be if it has a cumulative distribution functionMathworldPlanetmathPlanetmathPlanetmath which is absolutely continuousMathworldPlanetmath (http://planetmath.org/AbsolutelyContinuousFunction2).

Example:

Consider the event of throwing a coin. Thus, Ω={H,T} where H is the event in which the coin falls head and T the event in which falls tails.Let X=number of tails in the experiment. Then X is a (discrete) random variable.

Titlerandom variable
Canonical nameRandomVariable
Date of creation2013-03-22 11:53:10
Last modified on2013-03-22 11:53:10
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id21
Authormathcam (2727)
Entry typeDefinition
Classificationmsc 62-00
Classificationmsc 60-00
Classificationmsc 11R32
Classificationmsc 03-01
Classificationmsc 20B25
Related topicDistributionFunction
Related topicDensityFunction
Related topicGeometricDistribution2
Definesdiscrete random variable
Definescontinuous random variable
Defineslaw of a random variable
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