1. Draw the Markov chain corresponding to driving a car with a spare tire in the trunk with tire MTTF (Mean Time To have a Flat tire) of 1 month and 15 minute service time (time required to replace a flat tire with spare). Compute long term availability of driving this car by setting all state probability changes (derivatives) to zero at infinity. 2. Explain how Berger code can use smallest number of check bits out of all separable codes? 3. Write a list of things you would do, besides buying the highest quality COTS storage components and running them in properly cooled environment, in order to have very high availability such as reputable online cloud providers. Also write a list of “best practices” to follow considering observation from a very large number of disks operated by Google. 4. Compare and contrast RAID-Z levels, offered by ZFS to well known RAID levels in terms of tolerance to faults and performance. 5. Suggest a data replication system for storing the database of products in inventory of a chain store located in N cities nationwide. You may assume that the chain store has an e-commerce portal serving thousands of online customers. On the average, customers compare the specifications and prices of 10 items before they decide on one and order it. Which Fault Tolerance measure would you report to your supervisor and how do you compute the measure? State all your assumptions and explain briefly your reason to select voting strategy. 6. a. Compute row and column checksums for a 3x3 matrix A=[3 1 4, 1 5 9, 2 6 5] b. Modify (add or subtract) any one of the elements by some constant and locate the position of faulty element from row and column checksums c. Compute weighted row and column checksums d. Correct the faulty element from weighted row and column checksums 7. a. Which networking topology does FDDI networks use? b. Explain how FDDI networks achieve tolerance to fiber cable faults? c. How many cable breaks are allowed in FDDI networks before it is repaired at fault location? d. Which network measure changes in FDDI networks in case of a single cable fault?