The probability distribution of a discrete random variable can be characterized by its probability mass function. When the probability distribution of the random variable is updated, in order to consider some information that gives rise to a conditional probability distribution, then such a conditional distribution can be characterized by a conditional probability mass function.

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The following is a formal definition.

Definition Let and be two discrete random variables. The conditional probability mass function of given is a function such thatfor any , where is the probability that , given that .

You can find more details about the conditional probability mass function in the lecture entitled Conditional probability distributions.

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