Consider the fault of length L and the structure represented

Consider the fault of length L and the structure represented in the figure below. An earthquake on the fault may occur as a rupture of length s (assume s le L/4). The rupture may occur anywhere along the fault with equal likelihood, but may not extend beyond the known ends of the fault. Derive the CDF and PDF (in that order) of the shortest distance R (random variable) from the rupture to the power plant and apply the results to the following specific case: L = 200 mi, d = 10 mi, and s = 30 mi Plot the PDF and CDF of R using Mat lab. What is the probability that in the next earthquake generated by this fault, the shortest distance R will be less than or equal to 20 miles? An earthquake has occurred along the fault and the shorted distance from the fault rupture to the site of the power plant, R, is larger than 20 miles. What is the probability that R is lower than 50 miles? Make use of your results in (a) through (c).

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