The distribution of a discrete random variable can be characterized through its probability mass function (pmf). The probability that a given number will be the realization of a discrete random variable is equal to the value taken by its pmf in correspondence of that number.
In formal terms, the probability mass function of a discrete random variable is a function such thatwhere is the probability that the realization of the random variable is equal to .
Suppose a random variable can take only three values (1, 2 and 3), each with equal probability. Its probability mass function is
You can find an in-depth discussion of probability mass functions in the lecture entitled Random variables.
Related concepts can be found in the following glossary entries:
Joint probability mass function: the pmf of a random vector.
Marginal probability mass function: the pmf obtained by considering only a subset of the set of random variables forming a given random vector.
Conditional probability mass function: the pmf obtained by conditioning on the realization of another random variable.
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