# Isye 2027

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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 3 2 terms of the pmf are p(1) = λe−λ , p(2) = λ e−λ , and p(3) = λ e−λ . The Poisson distribution 2 6 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. B...
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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.

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