Figure 1 shows a sample path of a Poisson process where the sequence of random variables, {S1, S2, ...}, show the arrival times and the sequence, {X1, X2, ...}, consists of the interarrival times that are i.i.d. exponential random variables with E[X;] = 1/A. %3D S, S, X Š, Š, Figure 1: A sample path of a Poisson process. nd A such that S = AX where X = [X1 X2 X3 X4]" and S = [S1 S2 S3 Sa]" . Find fs(s) using fx(x) and A (a) (b) Hint: You may take the determinant of A as 1. 2.
Figure 1 shows a sample path of a Poisson process where the sequence of random variables, {S1, S2, ...}, show the arrival times and the sequence, {X1, X2, ...}, consists of the interarrival times that are i.i.d. exponential random variables with E[X;] = 1/A. %3D S, S, X Š, Š, Figure 1: A sample path of a Poisson process. nd A such that S = AX where X = [X1 X2 X3 X4]" and S = [S1 S2 S3 Sa]" . Find fs(s) using fx(x) and A (a) (b) Hint: You may take the determinant of A as 1. 2.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Figure 1 shows a sample path of a Poisson process where the sequence of random
variables, {S1, S2, ...}, show the arrival times and the sequence, {X1, X2, ...}, consists of the
interarrival times that are i.i.d. exponential random variables with E[X;] = 1/A.
%3D
3.
Š, Š,
S, S,
Figure 1: A sample path of a Poisson process.
nd A such that S = AX where X = [X1 X2 X3 X4]T and S = [S1 S2 S3 Sa]™.
Find fs(s) using fx(x) and A
(a)
(b)
Hint: You may take the determinant of A as 1.
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c0c65b8-afb7-4ed4-8c00-d498284fe5d7%2Fdc85685f-669f-4475-b01c-eb9bd3813ccc%2Fpl6vzyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Figure 1 shows a sample path of a Poisson process where the sequence of random
variables, {S1, S2, ...}, show the arrival times and the sequence, {X1, X2, ...}, consists of the
interarrival times that are i.i.d. exponential random variables with E[X;] = 1/A.
%3D
3.
Š, Š,
S, S,
Figure 1: A sample path of a Poisson process.
nd A such that S = AX where X = [X1 X2 X3 X4]T and S = [S1 S2 S3 Sa]™.
Find fs(s) using fx(x) and A
(a)
(b)
Hint: You may take the determinant of A as 1.
2.
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