conditional distribution

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For two jointly distributed random variables X and Y the conditional distribution of Y given X is the distribution of Y when X takes particular values. For discrete random variables it is given by

P[Y = y | X = x] = P[X = x, Y = y]/P[X = x].

For continuous random variables, the conditional density function is given by

f(y | x) = f(x, y)/f(x)

where f(x, y) is the joint density function, and f(x) is the marginal density function of X.

Subjects: Economics.

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