The probability distribution of a continuous random variable can be characterized by its probability density function. When the probability distribution of the random variable is updated, by taking into account some information that gives rise to a conditional probability distribution, then such a distribution can be characterized by a conditional probability density function.

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The following is a formal definition.

Definition Let and be two absolutely continuous random variables. The conditional probability density function of given is a function such thatfor any interval .

In the definition above the quantity is the conditional probability that will belong to the interval , given that .

More details about the conditional probability density function can be found in the lecture entitled Conditional probability distributions.

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