Poisson Distribution

Topics: Probability theory, Poisson distribution, Random variable Pages: 3 (754 words) Published: April 2, 2011
The Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business, number of customers in waiting lines, number of defects in a given surface area, airplane arrivals, or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies, e.g., to model the number of prairie dogs found in a square mile of prairie. The major difference between Poisson and Binomial distributions is that the Poisson does not have a fixed number of trials. Instead, it uses the fixed interval of time or space in which the number of successes is recorded.

Parameters: The mean is λ. The variance is λ.

[pic]

[pic] is the parameter which indicates the average number of events in the given time interval. Ex.1. On an average Friday, a waitress gets no tip from 5 customers. Find the probability that she will get no tip from 7 customers this Friday. The waitress averages 5 customers that leave no tip on Fridays: λ = 5. Random Variable : The number of customers that leave her no tip this Friday. We are interested in P(X = 7).

Ex. 2 During a typical football game, a coach can expect 3.2 injuries. Find the probability that the team will have at most 1 injury in this game. A coach can expect 3.2 injuries : λ = 3.2.
Random Variable : The number of injuries the team has in this game. We are interested in [pic].
Ex. 3. A small life insurance company has determined that on the average it receives 6 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day.

P(x ≥ 7) = 1 - P(x ≤ 6) = 0.393697

Ex. 4. The number of traffic accidents that occurs on a particular stretch of road during a month follows a Poisson distribution with a mean of 9.4. Find the probability that less than two accidents will occur on...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Probability distribution Essay
  • Binomial, Bernoulli and Poisson Distributions Essay
  • Essay about The Poisson Probability Distribution
  • Normal Distribution and Collective Premium Essay
  • Normal Distribution and Engineering Statistics Semester Essay
  • Analysis of Sickness Absence Using Poisson Regression Models Essay
  • Binomial Distribution and Conway Maxwell Poisson Essay
  • Normal Distribution Essay

Become a StudyMode Member

Sign Up - It's Free