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 total 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. To derive probabilities from observed frequencies, normalization is applied, which involves dividing the frequency of each outcome by the total number of observations ¹.

In practice, as the number of trials increases, the empirical distribution of outcomes tends to converge towards the theoretical PMF, illustrating the law of large numbers ².

If you have further questions about PMFs or related concepts, feel free to ask!