3 . [20] Dougie's car is worth 510,000. Dougie is a careless fellow who leaves the top down, the keys in the ignition, and his murse in the front seat. As a result, the probability of his car being stolen is 0.4. If his car is stolen, he will never get it back {the murse is actuallyr a knockoff bag full of expired coupons, assume that it has a value of zero}. Dougie has $200,000 in other wealth and his utility function for wealth is 1:.(w) = 201.1!\"'5. Suppose that Dougie can buy $K worth of insurance at a price of 33. 55K. [2] Write down Dougie's von NeumanMorgenstern utility function. [4] Is Dougie riskloving? Show your calculations. [6] How much insurance will he buy? [4] Does Dougie choose to fully insure? Explain why or why not. [4] Suppose instead that Dougie's utility function for wealth is 14w) = ln{u[w}). How would this impact the amount of insurance that he wants to buy? [DPPET?\