3. The occurrence of significant earthquakes [of magnitude 22 mo} in a region can be modeled with the Poisson distribution; that is, the probability of n earthquakes occurring over a duration equal to t is: p\" (I) : (hr?! n . Also, the magnitude of a significant earthquake is described by the shifted exponential distribution: exp[ht] FM(m)= lexp[(mmu)] for m 2 m0 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