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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10, 200 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10, 200 and $14, 700. a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)? b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)? c. What amount should you bid to maximize the probability that you get the property? d. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13, 100. If your objective is to maximize the expected profit, what is your bid? What is the expected profit for this bid (to 2 decimals)?
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