4.7 Poisson distribution (optional)

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 .05).