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 $15,100.
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 (in dollars)?
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 $12,750. If your objective is to maximize the expected profit, what is your bid?
Select What is the expected profit for this bid (in dollars)?
for uniform distribution parameter:a =9500and b=15100 |
a)
probability that 12000 bid be accepted =P(X<12000)=(x-a)/(b-a)=(12000-9500)/(15100-9500)= | 0.45 |
b)
probability that 14000 bid be accepted =P(X<14000)=(x-a)/(b-a)=(14000-9500)/(15100-9500)= | 0.80 |
c)
maximum bid for max probability =b= | 15100 |
d)
if someone will ing to give you 16000; expected bid to get max profit=(16000-9500)/2+9500= | 12750 |
expected profit =(16000-12750)*(12750-9500)/(15100-9500)= | 1886.16 |
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.
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