A Probability Mass Function (PMF) is a mathematical function that provides the probability distribution for discrete random variables. It maps each possible value of the random variable to its corresponding probability. For example, when rolling a fair six-sided die, the PMF assigns a probability of 1/6 to each outcome (1, 2, 3, 4, 5, 6) since there are six distinct outcomes in the sample space ².

The PMF is particularly useful for understanding the likelihood of different outcomes in scenarios where the variable can only take on specific, distinct values. It is important to note that the sum of all probabilities in a PMF must equal 1, ensuring that it represents a valid probability distribution ¹.

In practical applications, the PMF can be derived from observed frequencies by normalizing these frequencies, which involves dividing each frequency by the total number of observations ¹. This normalization process allows for the conversion of raw counts into probabilities, making the PMF a fundamental tool in statistics and probability theory.