Final answer:
The frequency function of a discrete random variable, also known as the probability mass function, provides the probabilities of occurrence of different possible outcomes. This function satisfies two conditions: probability values between zero and one, inclusive, and the total sum of probabilities equaling one.
Step-by-step explanation:
The frequency function of a discrete random variable is indeed equivalent to the probability mass function (PMF). The PMF provides the probabilities of occurrence of different possible outcomes for a discrete random variable. It is a function that gives the probability that a discrete random variable is exactly equal to some value.
In comparison, the probability distribution function (PDF) is a broader concept that applies to both discrete and continuous random variables. However, in the context of discrete random variables, PDF and PMF are often used interchangeably.
In summary, the PMF of a discrete random variable will satisfy two conditions: (1) the probability of each outcome is between zero and one, inclusive; and (2) the sum of all these probabilities equals one. These are the defining characteristics of a discrete probability distribution.
When graphed, the PMF will only have value at integers or other countable outcomes, reflecting the discrete nature of the random variable.