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3. An oil company owns. some land that is purported to contain oil. The company classifies such land into four categories by the total number of barrels that are expected to be obtained from the well; a 500,000-barrel well ( 0, ), a 200,000-barrel well ( 02 ), a 50,000-barrel well (0, ), or a dry well (0,). The company is faced with deciding whether to drill for oil ( a, ), to unconditionally lease the land to an independent oil driller ( a, ), or to conditionally lease the land at a rate depending upon the oil strike ( a; ). The cost of drilling a producing well is $100,000 and the cost of drilling a dry well is $75,000. For producing wells the profit per barrel of oil is $1.50 (after deducting all production costs). Under the unconditional lease arrangement, the company receives $45,000 for the land, whereas under the conditional lease arrangement the company receives 50 cents for each barrel of oil extracted, provided the land yields a 200,000- or 500,000-barrel strike; otherwise it receives nothing. The company has had some experience with wells in similar geographical areas and has concluded that about 10 percent of the strikes are 500,000-barrel wells, 15 percent are 200,000-barrel wells, 25 percent are 50,000-barrel wells, and 50 percent are dry wells. a. (i) Calculate the Loss matrix, L(0, a) for the given problem. [ Recall that a gain is a negative loss. ] [5] (ii) Determine #(0) from the given information. [2] (ili) Find the Bayes Rule for the no data problem. [5]