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Poisson Distribution. A Poisson random variable is the number of successes that result from a Poisson experiment. The probability distribution of a Poisson random variable is called a Poisson distribution. Given the mean number of successes (Î¼) that occur in a specified region, we can compute the Poisson probability based on the following formula:
The expression pX(x) is a function that assigns probabilities. to each possiblevalue x; thus it is oftencalled the probability function for the random variable X. 1.3. Probability distribution for a discrete random variable. The probability distribution for a. discrete random variable X can be represented by a formula, a table, or a graph, which provides. pX(x)=P(X=x)forallx.