Probability Mass Function
A Probability Mass Function (PMF) is a mathematical function that gives the probability of a discrete random variable taking on a specific value. It assigns a probability to each possible outcome, ensuring that the sum of all probabilities equals one. For example, if you roll a fair six-sided die, the PMF would assign a probability of \frac16 to each of the outcomes 1, 2, 3, 4, 5, 6.
The PMF is essential in statistics and probability theory, as it helps in understanding the distribution of discrete random variables. It is often used in various applications, such as game theory, risk assessment, and decision-making processes. By analyzing the PMF, one can make informed predictions about the likelihood of different outcomes.