Conditional probability distribution: Difference between revisions

Revision as of 16:04, 4 March 2004

Revision as of 17:57, 6 March 2004

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The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: [[Borel's paradox]] shows that conditional probability density functions need not be invariant under coordinate transformations.

If for discrete random variables ''P''(''Y''=''y''|''X''=''x'')=''P''(''Y''=''y'') for all ''x'' and ''y'', or for continuous random variables ''p''_''Y''|''X''(''y''|''x'')=''p''_''Y''(''y'') for all x and y, then ''Y'' is said to be [[Statistical independence|independent]] of ''X'' (and this implies that ''X'' is also independent of ''Y'').