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Lecture 4

Week 4 EC255.docx

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Wilfrid Laurier University
Alex Lun

EC255 Week 4 5.4 POISSON DISTRIBUTION -The binomial distribution describes a distribution of two possible outcomes designated as success and failure from a given number o trials -The Poisson distribution focuses only on the number of secrete occurrences over some interval or continuum -A Poisson experiment does not have a given number of trials (n) as a binomial experiment does -The Poisson distribution describes the occurrence of rare evens – has been referred to as the law of improbable events -It is often used to describe the number of random arrivals per some time interval -If the number of arrivals per interval is too frequent, the time interval can be reduced enough so that a rare number of occurrences is expected -The Poisson distribution has the following characteristics: -It is a discrete distribution -It describes rare events -Each occurrence is independent of the other occurrences -It describes discrete occurrences over a continuum or interval -The occurrences in each interval can range from zero to infinity -The expected number of occurrences must hold constant throughout the experiment -Ex. Number of telephone calls per minute at a small business -Ex. Number of times a 1-year old personal computer printer breaks down per quarter -Each example represents a rare occurrence -Time is a more common interval, but intervals can range – some of the intervals may have zero occurrences -If a Poisson distributed phenomenon is studied over a long period of time, a long-run average can be determined – this is lambda -Each Poisson problem contains a lambda value from which the probabilities of particular occurrences are determined -The researcher must be specific about which lambda is used because it could range from day to day Using the Poisson Tables -Every value of lambda determines a different Poisson distribution -Regardless of the nature of the interval associated with a lambda, the Poisson distribution for a particular lambda is the same Mean and Standard Deviation of a Poisson Distribution -The mean or expected value of a Poisson distribution is lambda -It is the long-run average of occurrences for an interval if many random samples are taken -Lambda is usually n
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