A one-parameter, discrete frequency distribution giving the probability that n points (or events) will be (or occur) in an interval (or time) x, provided that these points are individually independent and that the number occurring in a subinterval does not influence the number occurring in any other nonoverlapping subinterval. It has the form P(n, x) = e^−κx(κx)ⁿ/n!. The mean and variance are both κx, and κ is the average density (or rate) with which the events occur. When κx is large, the Poisson distribution approaches the normal distribution. The binomial distribution approaches the Poisson when the number of events n becomes large and the probability of success p becomes small in such a way that np → κx. The Poisson distribution arises in such problems as radioactive and photoelectric emissions, thermal noise, service demands, and telephone traffic.