3. Exercise 06.07 Algorithmic eBook Exercise 6.7 (Algorithmic) Suppose we are in

Question

3. Exercise 06.07 Algorithmic eBook Exercise 6.7 (Algorithmic) 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 $9,600 will be accepted Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,600 and $14,900 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 $12,800. If your objective is to maximize the expected profit, what is your bid? Select your answer What is the expected profit for this bid (to 2 decimals)?

Explanation / Answer

Ans:

Cumulative distribution for unifrom distribution:

F(x)=P(X<=x)=(x-a)/(b-a)

a)F(12000)=(12000-9600)/(14900-9600)=2400/5300=0.45

b)F(14000)=(14000-9600)/(14900-9600)=4400/5300=0.83

c)x=14900 for maxize the probability to win the bid

as F(14900)=(14900-9600)/(14900-9600)=1

d)F(12800)=(12800-9600)/(14900-9600)=0.6

F(16000)=1

16000*1=16000

Bid should be 16000 for maximum expected profit.

Expected profit=16000-9600=6400

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