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5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and C3 fail with probability P2 = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C₁ C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Øy, dy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, μ2, µ3; O1, O2, O3; 8₁, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to infinity, to minus infinity or to any real positive or negative value?

5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and C3 fail with probability P2 = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C₁ C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Øy, dy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, μ2, µ3; O1, O2, O3; 8₁, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to infinity, to minus infinity or to any real positive or negative value?

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
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5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and c3 fail with probability P₂ = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C1 C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Oy, Sy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, M2, M3; O₁, O2, O3; 81, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to infinity, to minus infinity or to any real positive or negative value?
Transcribed Image Text:5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and c3 fail with probability P₂ = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C1 C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Oy, Sy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, M2, M3; O₁, O2, O3; 81, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to infinity, to minus infinity or to any real positive or negative value?
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