F x y PX x Y y

is known as the conditional PDF of X; it gives the probability that X takes on the value of x given that Y has assumed the value y. Similarly, f (y | x) = P(Y = y | X = x)

which gives the conditional PDF of Y.

The conditional PDFs may be obtained as follows:

As the preceding expressions show, the conditional PDF of one variable can be expressed as the ratio of the joint PDF to the marginal PDF of another (conditioning) variable.

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