Question

Explain the concepts of joint probability mass function and marginal probability function for two discrete
random variables with the help of an example

03 Aug 2026
Answer :
Word Count : 592
In probability theory, when two discrete random variables are considered together, their combined behaviour is described using the joint probability mass function. It provides information about the probability that two random variables take specific values simultaneously. Let X and Y be two discrete random variables defined on the same sample space. The joint probability mass function (joint PMF) of X and Y is denoted by p(x, y) and is defined as p(x, y) = P(X = x, Y = y) where x and y represent the possible values of X and Y. The joint PMF gives the probability that X assumes the value x and at the same time Y assumes the value y. Since probabilities cannot be negative, p(x, y) ≥ 0 for all values of x and y.
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