(3.4) A rm owns two buildings which have the same value (W0 = 40 for each building) and which are subjected to a risk of full loss with identical probability %. Because these buildings are located far away from each other the lisks are independent. The risk manager has a budget of 8 to spend on insurance premia in order to cover the risks. (a) If he covers the rst building at a coinsurance rate ,3; = 0.6, which coinsurance rate will he obtain for building 2'? (b) What is the coinsurance rate identical for each building (i.e. ,3 = 31 = g) that yields the same premium '? (c) Show thatwhatever the total budget availablea risk averter should always select ,61 = g. As usual, the proof is done by drawing the cumu- lative distributions of nal wealth. This result illustrates the intuitive idea that one should \"never gamble with one's insurance budget.\