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Poisson

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.

The Poisson distribution may is derived by considering an interval, in time, space or otherwise, in which events happen at random with a known average number. The interval is divided in n subintervals of equal size. The probability that an event will fall in the subinterval is for each k equal to λ/n and the occurrence of an event Ik may be approximately considered to be a Bernoulli trial.

In cases where n is very large and p is very small, the distribution may be approximated by the less cumbersome Poisson distribution. This approximation is sometimes known as the law of rare events since each of the n individual Bernoulli events rarely occurs. The word law in statistics is sometimes used as a synonym of probability distribution and convergence in law means convergence in distribution. 

Waiting time in a single server queue

Using a single-server queuing system with Poisson arrivals of 10 units per hour and a constant service time of 2 minutes per unit. How do I go about calculating how long the customer waiting time will be in seconds, on average?

Incoming Call Poisson Distribution

The number of incoming phone calls at a company switchboard during 1-minute intervals is believed to have a Poisson distribution. Use a=.10 and the following data to test the assumption that the incoming phone calls follow a Poisson distribution. # of Incoming Phone Calls During a 1-min Interval Observed Frequency 0

Poisson distribution of a geiger counter

A Geiger counter used in a spent nuclear fuel area records on the average of 40 counts per min. Determine the probability that there will be 2 counts in a 6-sec period.