The Hayward campus has become a dangerous place for people on motorized scooters. There are six intersections on the campus loop, independent of one another, for which accidents occur following a Poisson process with different rates, say A₁,..., A6, per week. The Board of Campus Safety is interested in the total number of accidents that occur next semester (sixteen weeks). (a) Using the moment generating function, derive the distribution of the total number of accidents that occur next semester at these intersections combined. Make sure you define all variables used. (b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9, 0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146 (inclusively) accidents on the campus loop next semester? (c) What is the expected value and standard deviation for the number of accidents on the campus loop next quarter?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
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6. The Hayward campus has become a dangerous place for people on motorized scooters. There
are six intersections on the campus loop, independent of one another, for which accidents occur
following a Poisson process with different rates, say A₁,..., A6, per week. The Board of Campus
Safety is interested in the total number of accidents that occur next semester (sixteen weeks).
(a) Using the moment generating function, derive the distribution of the total number of
accidents that occur next semester at these intersections combined. Make sure you define
all variables used.
(b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9,
0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146
(inclusively) accidents on the campus loop next semester?
(c) What is the expected value and standard deviation for the number of accidents on the
campus loop next quarter?
Transcribed Image Text:6. The Hayward campus has become a dangerous place for people on motorized scooters. There are six intersections on the campus loop, independent of one another, for which accidents occur following a Poisson process with different rates, say A₁,..., A6, per week. The Board of Campus Safety is interested in the total number of accidents that occur next semester (sixteen weeks). (a) Using the moment generating function, derive the distribution of the total number of accidents that occur next semester at these intersections combined. Make sure you define all variables used. (b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9, 0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146 (inclusively) accidents on the campus loop next semester? (c) What is the expected value and standard deviation for the number of accidents on the campus loop next quarter?
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