# Find the mean and the pdf of s solution first we

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Unformatted text preview: with rate λ > 0. (a) Find the probability there is exactly one count in each of the intervals (0,1], (1,2], and (2,3]. (b) Find the probability of the event A, that there are two counts in the interval (0, 2] and two counts in the interval (1, 3]. Note that these intervals overlap. (c) Find the conditional probability there are two counts in the interval (1,2], given that there are two counts in the interval (0,2] and two counts in the the interval (1,3]. Solution (a) The numbers of counts in the these disjoint intervals are independent, Poisson random variables with mean λ. Thus, the probability is (λe−λ )3 = λ3 e−3λ . (b) The event A is the union of three disjoint events: A = B020 ∪ B111 ∪ B202 , where Bijk is the event that there are i counts in the interval (0, 1], j counts in the interval (1, 2], and k counts in the interval (2, 3]. Since the events Bijk involve numbers of counts in disjoint intervals, we can easily write down their probabilities. For example, P (B020 )...
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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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