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Question: Let T_A, T_B, and Tc be the failure times of components A, B, and C. Assume these are independent exponential random variables with rates α, β, and γ, respectively.

a) What is the distribution of the time until the first failure?

b) What is the probability that the first component to fail is component C.

c) Given that the first component to fail is component C, what is the distribution of the time between the first and second failures?

d) Write a formula for the (unconditional) c.d.f. of the time between the first and second failures.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M92640088

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