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Problem 5 (20 points): About the RAID-6 System is comprised of 5 disk drives for storing data. The system is functional as long as 3 drive are good. Hence it is also known as 3-out-of-5 active redundant system where "active" means all these five drives are in "on" mode at any time. Let r(t) be the reliability of each disk drive in year t. Do the following: 1) Present the reliability function of the RAID-6 system using the disk drive reliability function is r(t). 2) Estimate the reliability of the RAID-6 system by the end of 10 years if r(t=10 years )=0.8. 3) If the reliability of RAID-6 system target to be 0.9 by the end of 100 years, what is the minimum required reliability of r(t) so as to achieve this target. 4) If the mean lifetime (or mean time to failure = MTTF) of a disk drive is 100 years, what is the mean lifetime (or MTTF) of the entire RAID-6 system? 3-out-of-5 RAID-6 system Note: Disks 1-3 are active disks and Disks 4-5 are redundant disks Figure 5: The Configuration of A RAID-6 System