(1 point) Consider a system with one component that is subject to failure, and s

Question

(1 point) Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 25 days, and that we replace the component with a new copy immediately when it fails. (a) Approximate the probability that the system is still working after 3625 days Probability (b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5). Approximate the probability that the system is still working after 4250 days. Probability

Explanation / Answer

we have to find out the poisson's probability of each component as they folllow exponential distribution

=25 days

probabiltythat system is working after 3625 days

3625/120=30.21 =31 =expected no. of days each component will work

P=2531*e-25 /31! =9.07799E-05

time to replace one component=0.5/120= 0.0042

total time to relace= 0.0042*119 = 0.5

expected no of days each component will work = 4250-0.5= 4249.5/120 =35

P= 2535*E-25/35!

0.011384281

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