Question

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 $9,900 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,900 and $15,500.

1. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
2. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
3. What amount should you bid to maximize the probability that you get the property (in dollars)?
   
   
4. 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 $12,950. If your objective is to maximize the expected profit, what is your bid?
   
   
   What is the expected profit for this bid (in dollars)?

Answer 1