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Problem 5. A system suffers faults by a Poisson process with rate X. Each fault will, independently, cause the system to fail after time X with c.d.f. F. When the system fails, the responsible fault is fixed, but earlier other faults may remain and cause later failure. (a) What is the distribution of the number of failures up to t? (b) What is the distribution of the number of faults that remain in the system at time t and are not yet fixed? (c) Are the random variables in parts (a) and (b) dependent or independent? (justify!)

Problem 5. A system suffers faults by a Poisson process with rate X. Each fault will, independently, cause the system to fail after time X with c.d.f. F. When the system fails, the responsible fault is fixed, but earlier other faults may remain and cause later failure. (a) What is the distribution of the number of failures up to t? (b) What is the distribution of the number of faults that remain in the system at time t and are not yet fixed? (c) Are the random variables in parts (a) and (b) dependent or independent? (justify!)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 5. A system suffers faults by a Poisson process with rate X. Each fault will, independently, cause the system to fail after time X with c.d.f. F. When the system fails, the responsible fault is fixed, but earlier other faults may remain and cause later failure. (a) What is the distribution of the number of failures up to t? (b) What is the distribution of the number of faults that remain in the system at time t and are not yet fixed? (c) Are the random variables in parts (a) and (b) dependent or independent? (justify!)
Transcribed Image Text:Problem 5. A system suffers faults by a Poisson process with rate X. Each fault will, independently, cause the system to fail after time X with c.d.f. F. When the system fails, the responsible fault is fixed, but earlier other faults may remain and cause later failure. (a) What is the distribution of the number of failures up to t? (b) What is the distribution of the number of faults that remain in the system at time t and are not yet fixed? (c) Are the random variables in parts (a) and (b) dependent or independent? (justify!)
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