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Narky Blert (talk | contribs) dab-needed tag |
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The conditional probability of ''Y'' being in ''A'' is given by
:<math>P(Y \in A | X = x) = \frac{\int_A f_{X,Y}(x, y) \mathrm{d}y}{\int_\mathbb{R} f_{X,Y}(x, y) \mathrm{d}y}.</math>
Conditional probability is a two variable function as before, undefined outside of the [[support (mathematics)|support]]
Note that this is not the same as conditioning on the event <math>B = \{X = x\}</math>, but is rather a limit: see [[Conditional probability#Conditioning on an event of probability zero]].
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