A Conditional Probability Mass Function

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The probability mass function of a pair of discrete random variables is the function . The conditional mass function of given is the function . Thus the mass function (left-hand plot) computes probabilities of intersections, while the conditional mass function (right-hand plot) computes conditional probabilities. For each value, the slice through the conditional mass function at that value gives the distribution of when assumes the value . The mean of this distribution is the conditional expectation of given , . The weighted average of the conditional expectations, with the weights given by the probability that InlineMath, is the expected value of .


You can reverse the roles of and to obtain the conditional mass function of given and the conditional expectation of given .


Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA



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