The occurrence of signicant earthquakes [of magnitude Emu) in a region can be modeled with the Poisson distribution; that is, the probability of n earthquakes occurring over a duration equal to r is: UH)\" n! Also, the magnitude of a signicant earthquake is described by the shifted exponential distribution: M) = explsil FM (:11) = l exp[(m mun for m 2 m\" where ,6 is a constant. Assuming that the number of earthquakes and the magnitude are statistically independent random variables, derive the probability distribution function of the annual maximum earthquake magnitude in the pertinent region