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Lecture 4

# Week 4 EC255.docx

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Wilfrid Laurier University

Economics

EC255

Alex Lun

Fall

Description

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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