<Table> <Tr> <Td> </Td> <Td> This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (July 2011) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (July 2011) (Learn how and when to remove this template message) </Td> </Tr> <P> In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment . In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events . For instance, if the random variable X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey . </P> <P> A probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed . The sample space may be the set of real numbers or a higher - dimensional vector space, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be (heads, tails). </P>

Is a description of how probabilities are distributed over the values of a random variable