4.6 Poisson distribution

a discrete random variable (RV) that counts the number of times a certain event will occur in a specific interval; characteristics of the variable: The probability that the event occurs in a given interval is the same for all intervals. The events occur with a known mean and independently of the time since the last event. The distribution is defined by the mean μ of the event in the interval. Notation: X ~ P ( μ ). The mean is μ = np . The standard deviation is σ  =  μ . The probability of having exactly x successes in r trials is P ( X = x ) = ( e − μ ) μ x x ! . The Poisson distribution is often used to approximate the binomial distribution, when n is “large” and p is “small” (a general rule is that n should be greater than or equal to 20 and p should be less than or equal to 0.05).