Question

Q3. Commodore 64's computer has three critical parts, each of which is needed for the computer to work. The computer runs continuously as long as the three required parts are working. The three parts have mutually independent exponential lifetimes before they fail. The expected lifetime of parts 1, 2 and 3 are 10 weeks, 20 weeks and 30 weeks, respectively. When a part fails, the computer is shut down and an order is made for a new part of that type. When the computer is shut down (to order a replacement part), the remaining two working parts are not subject to failure. The time to replace part 1, part 2 and part 3 are distributed with mean 1 week; 2 weeks and 3 weeks respectively. exponentially Assuming that all parts are initially working, what is the expected time until the first part fails? 10min What is the probability that part 1 is the first part to fail? What is the long-run proportion of time that the computer is working? [10 pts] i. [10 pts] 1 [10 pts] i. iii.

Answer 1

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