(Solved): uppose we are interested in bidding on a plece of land and we know one other bidder is interested. ...

uppose we are interested in bidding on a plece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $$\$10$$, 000 ili be accepted. Assume that the competitor's bid $$x$$ is a random variable that is uniformly distributed between $$\$10,000$$ and $$\$15,000$$. (a) Suppose you bid $$\$12,000$$. What is the probability that your bid will be accepted? (b) Suppose you bid 513,000 . What is the probability that your bid will be accepted? (c) What amount should you bid in dollars to maximize the probability that you get the property? $$5$$ (d) Suppose you know someone who is willing to pay you $$\$16,000$$ for the property. What is the expected profit in dollars if you bid the amount given in part (c)? 5 Find a bid in dollars which produces a greater expected profit than bidding the arnount given in part (c). (IIf an answer does not exist, enter DNE.) 5 Would you consider bidding less than the amount in part (c)? Why of why not? Yes. There is a bid which gives a greater expected prosit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c). No. The bid which maximizes the expected profit is the amount $$g$$ ven in part (c), thus it does not make nense to place a smaller bid.