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9. (a) A structure consists of 100 column footings. Suppose the settlement of each footing is exponentially distributed with a mean of 2 inches and the settlements between footings are statistically independent. What is the probability that the maximum settlement S among the 100 footings will not exceed 5.0 inches? Compare this exact probability with the answer obtained assuming an appropriate asymptotic distribution for S. (b) What is the probability that the minimum settlement S is at least 0.5 inch? (c) Determine the mean and coefficient of variation of the maximum differential settlement A defined as (S,- S )