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Line 11: If for discrete random variables ''P''(''Y''=''y''\|''X''=''x'')=''P''(''Y''=''y'') for all ''x'' and ''y'', or for continuous random variables ''p''<sub>''Y''\|''X''</sub>(''y''\|''x'')=''p''<sub>''Y''</sub>(''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''). Seen as a function of ''y'' for given ''x'', ''P''(''Y''=''y''\|''X''=''x'') is a probability and so the sum over all ''y'' (or integral if it is a density) is 1. Seen as a function of ''x'' for given ''y'', it is a [[likelihood]], so that the sum over all ''x'' need not be 1.

Conditional probability distribution: Difference between revisions