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Unformatted text preview: ith pmf
−λ k
p(k ) = e k!λ for k ≥ 0. In particular, 0! is deﬁned to equal one, so p(0) = e−λ . The next three
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terms of the pmf are p(1) = λe−λ , p(2) = λ e−λ , and p(3) = λ e−λ . The Poisson distribution
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arises frequently in practice, because it is a good approximation for a binomial distribution with
parameters n and p, when n is very large, p is very small, and λ = np. Some examples in which
such binomial distributions occur are:
• Radio active emissions in a ﬁxed time interval: n is the number of uranium atoms in a
rock sample, and p is the probability that any particular one of those atoms emits a particle
in a one minute period.
• Incoming phone calls in a ﬁxed time interval: n is the number of people with cell
phones within the access region of one base station, and p is the probability that a given such
person will make a call within the next minute.
• Misspelled words in a document: n is the number of words in a document and p is the
probability that a given word is misspelled.
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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