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 $15,000.
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?