Poisson Distribution |
|
The poisson distribution is used to model rates, such as rabbits per acre,
defects per unit, or arrivals per hour. The poisson distribution is
closely related to the exponential distribution. If x is a poisson
distributed random variable, the 1/x is an exponential random variable.
If x is an exponential random variable, then 1/x is a poisson
random variable. For a random variable to be poisson distributed, the
probability of an occurrence in an interval must be proportional to the length
of the interval, and the number of occurrences per interval must be independent.
The poisson probability density function is Microsoft Excel contains the poisson probability distribution function. The format is =POISSON(x, m,0) The term p(x,m) represents the probability of exactly x occurrences in an interval having an average of m occurrences. The mean and variance of the poisson distribution are both equal to m. The poisson cumulative distribution function is simply the sum of the poisson probability density function from 0 to x. The cumulative poisson distribution has been computed in many text books to eliminate the need for tedious calculations, but most people prefer to use the Excel formula =POISSON(x, m,1) Example Solution Click here to download this solution and the remaining examples on this page in Microsoft Excel. Example Solution The probability of exactly 3 errors in 15,000 lines of randomly selected lines of code is Example Solution =POISSON(2,3,1) The "1" at the end of this formula gives the cumulative poisson. The probability of more than 2 errors is equal to the probability of exactly 3 plus the probability of exactly 4 plus the probability of exactly 5, etc. A simpler approach is to consider that the probability of more than 2 errors is equal to one minus the probability of 2 or fewer errors. Thus, the probability of more than 2 errors is 1 - 0.4232 = 0.5768. |