# Probability Distribution

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.

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