Binomial Distribution and Probability (S2 Watch

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A database has 1,000,000 records, which occupy disk storage at a density of 10 records per block; that is, the database occupies 100,000 disk memory blocks, each block containing 10 database records. You are told that a weekly update modifies 3% of the records, and that each record is modified independently of the others, the changes being distributed uniformly across the records; that is, all records have the same probability of being modified during the weekly update.
Answer the following questions:
1. Consider a given block and let X be the random variable that counts the number of records (0 up to 10) of the block that are changed during the weekly update.
(a) Justify why X has a binomial distribution with parameters n = 10 (number of trials) and p = 0.03 (probability of success). (5 marks)
(b) Write a general expression for P(X = r), i.e., the probability that exactly r records in the given block are changed during the weekly update. (5 marks).
(c) What is the probability that the given block is changed during the weekly update? Justify your answer by presenting all cal- culations. You can use the following approximation: (0.97)10 = 0.73742. (25 marks)
2. What is the expected total number of blocks that are changed during
the weekly update?
(15 marks)

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