Question: In Reliability Ques (March 2004), the exponential distribution was used to model the lengths of life of CD-ROM drives in a two-drive system. The two

In Reliability Ques (March 2004), the exponential was used to model the lengths of life of CD-ROM drives in a two-drive system. The two CD-ROM drives operate independently, and at least one drive must be operating for the system to operate successfully. Both drives have a mean length of life of 25,000 hours.
a. The reliability R(t) of a single CD-ROM drive is the probability that the life of the drive exceeds t hours. Give a formula for R(t).
b. Use the result from part a to find the probability that the life of the single CD-ROM drive exceeds 8,760 hours (the number of hours of operation in a year).
c. The reliability S(t) of the two-CD-ROM-drive system is the probability that the life of at least one drive exceeds t hours. Give a formula for S( t ).
d. Use the result from part c to find the probability that the two-drive CD-ROM system has a life whose length exceeds 8,760 hours.
e. Compare the probabilities you found in parts b and d.

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