In probability and statistics, a probability distribution assigns a probability to each of the possible outcomes of a random experiment. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution is a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution is a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous-time, may demand the use of more general probability measures.
In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:
- by supplying a valid probability mass function or probability density function
- by supplying a valid cumulative distribution function or survival function
- by supplying a valid hazard function
- by supplying a valid characteristic function
- by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.
Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.