(3.5) Consider again the data of the previous exercise and rst express the pre- mium and the distribution of nal wealth when the risk manager selects a deductible of 20 for each building (assume the loading is zero to simplify the computation). Now, his insurer suggests an \"umbrella policy\" where, for the same premium, you receive a coverage with a deductible of 22.85 on the aggregate loss. (a) Check that indeed this umbrella policy induces an actuarially fair pre- mium of 10. (1)) Again by drawing the cumulative distribution function of nal wealth, show thatas compared to the separate deductiblesthe umbrella pol- icy reduces the risk without changing the expected nal wealth