High Quality Content by WIKIPEDIA articles! Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value. 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 fY(y | X=x) = fY(y) for all x and y, then Y is said to be independent of X.

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