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 $9,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,500 and $15,200.

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)?

What is the expected profit for this bid (in dollars)?

Answer 1

a) probability that your bid will be accepted=(12000-9500)/(15200-9500)=0.44

b) probability that your bid will be accepted =(14000-9500)/(15200-9500)=0.79

c) maximize the probability that you get the property ; bid =15200