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?
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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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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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