Chapter 6 Homework Problems Graded Assignment | Back to Assignment Due Monday 02

Question

Chapter 6 Homework Problems Graded Assignment | Back to Assignment Due Monday 02.26.18 at 12:00 PM Attempts Keep the Highest: /s 3. Exercise 08.07 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 wil 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 (e) but a friend suggests you bid $12,80o. If your object is to maximize the expected profit, what is your bid? Stay with your bid in part fcl it mainizes expected proft is the expected profit for this bid (to 2 decimals)? Session

Explanation / Answer

a) probability P(X<14000)=(12000-9600)/(14900-9600)=0.45

b)

P(X<14000) =(14000-9600)/(14900-9600)=0.83

c)

amount bid to maximize probability of win =14900

d)

bid for maximum profit =(16000+9600)/2 =12800; hence bid $12800 to maximize profit/

e) expected proft =(16000-12800)*(12800-9600)/(14900-9600)=$ 1932.08

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