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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.
- Spring '08
- The Land