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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:
For example, 1  X represents the random variable X. 2  P(X) represents the probability of X. 3  P(X = x) refers to the probability that the random variable X is equal to a particular value, denoted by x.4  As an example, P(X = 1) refers to the probability that the random variable X is equal to 1.t would be the probability that the coin flip experiment results in zero heads. the probability that the experiment results in one head. P(X. 1) = P(X = 0) + P(X = 1) = 0.25 + 0.50 = 0.75. Like a probability distribution, a cumulative probability distribution can be represented by a table or an equation.