A probability distribution is a mathematical function that describes the likelihood of different outcomes in a random event. It provides a list of probabilities associated with each possible value or range of values for a random variable, which can be either discrete or continuous.

For discrete random variables, the probability distribution is often represented as a probability mass function (PMF), which assigns probabilities to each possible outcome. For example, when tossing a coin, the outcomes can be heads or tails, and the PMF would assign a probability to each outcome based on the likelihood of occurrence.

In contrast, continuous random variables are described using a probability density function (PDF), which indicates the probability of the variable falling within a particular range of values. The cumulative distribution function (CDF) is another way to represent probabilities, showing the probability that a random variable takes on a value less than or equal to a specific point.

Understanding probability distributions is essential in statistics and data science, as they form the foundation for making inferences and predictions based on data ³⁵.