(a) Suppose that X and Y have the joint CDF: FXy(m,y) = [1 + e'f + e'y)_1. (i) Find the marginal CDFs for X and Y, and the copula function C(o,o] for X and Y. {4 marks] (ii) Find the coefcients of lower and upper tail dependency for this copula. (3 marks) (b) You work for a large reinsurance company and you are responsible for building statistical models to estimate the joint probability of intensity of tropical cyclone wind and rainstorms. The intensity of wind and rainstorms are two major sources of damage and loss. You collect data on rainfall and wind velocity Over 200 days during tropical cyclones. You are given that wind velocity {in m/s} follows a LogNormal distribution with parameters ,u = 3 and o = 0.25, and that daily rainfall (in mm) follows a Weibull distribution with parameters 9 = 230 and 1 21.2. You use the following copula to model the dependence structure between daily rainfall and wind velocity: _ 1511.152 Club \"2) 1 9(1 mm v.2) Using method of moments, you estimate 6" = 0.70. Based on this estimate, use the above copula to calculate the joint probability that daily rainfall exceeds 110mm and wind velocity exceeds 25 m/s