Random variable: Difference between revisions

Revision as of 08:32, 1 June 2004

Revision as of 08:32, 1 June 2004

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=== Distribution functions ===

If a random variable ''X'':Ω->'''R''' defined on the probability space (Ω, ''P'') is given, we can ask questions like "How likely is it that the value of ''X'' is bigger than 2?". This is the same as the probability of the event {''s'' in Ω : ''X''(''s'') > 2} which is often written as ''P''(''X'' > 2) for short.

Recording all these probabilities of output ranges of a real-valued random variable ''X'' yields the [[probability distribution]] of ''X''. The probability distribution "forgets" about the particular probability space used to define ''X'' and only records the probabilities of various values of ''X''. Such a probability distribution can always be captured by its [[cumulative distribution function]]