4 (10 points) (a) Suppose the annual maximum wind speed in Miami, FL can be modeled with a GEV distribution, and the maximum winds in different years are independent. Derive the return level for the annual maximum wind (in terms of (mean) return period T (yr) and GEV parameters, for both cases when shape parameter is equal to and not equal to zero). (5 points) (b) Suppose the highest winds in Miami are caused by tropical cyclones (TCs), which have an annual frequency 2 and arrive proximately as a Poisson process. Suppose the probability that the (peak) wind of a Miami TC is greater than u is ( , and the extremes of these winds above the threshold u can be modeled with a GPD. Derive the return level for the annual maximum wind (in terms of (mean) return period T (yr), GPD parameters, and ( , for both cases when shape parameter is equal to and not equal to zero). (5 points)