Discrete distributions are statistical functions that describe the probabilities of outcomes for discrete random variables, which can take on a countable number of values. Common examples include the binomial distribution, which models the number of successes in a fixed number of trials, and the Poisson distribution, which represents the number of events occurring in a fixed interval of time or space. These distributions are characterized by their probability mass functions (PMFs), which assign probabilities to each possible value of the random variable. Discrete distributions are essential in various fields, including statistics, economics, and engineering, as they help in making predictions and informed decisions based on finite data sets.