Problem 4 The epicenter of an earthquake occurs randomly along a fault. Let R denote the distance from a site to the epicenter of a future earthquake. The geometry of the site relative to the fault and the epicenter is given in the figure below. Let X denote the location of the epicenter in the coordinate system shown in the figure. X 20/3 U/3 Fault Epicenter R d Site (a) Assuming that the epicenter is equally likely to occur anywhere along the fault, derive analytically the PDF and CDF of R using the theory about the function of a random variable (in contrast with the geometric approach used previously for this type of problems). (b) Using the following parameter values: {= 120 km and d = 20 km (i) Plot the PDF and CDF derived under (a). (ii) Determine the median value of R. (iii) Determine the 10 percent fractile of R