Suppose we are interested in bidding on a piece of land and we know one other bi

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 $9,600 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,600 and $15,200.

Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?

What amount should you bid to maximize the probability that you get the property?
$

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 -Stay with your bid in part (c); it maximizes expected profitBid $12800 to maximize the expected profitItem 4

What is the expected profit for this bid (to 2 decimals)?
$

Explanation / Answer

f(x) = (1/(15,200 - 9600))/0 (elsewhere) = 1/5600

a) P(10,000 < x < 12,000) = 2000(1/5600) = .0.36

b) P(10,000 < x < 14,000) = 4000(1/5600) = 0.71

c) Other person can bid $15,200. So, you should bid $15,201

d) Bid, 12800

e) Expected profit = ($16,000 - Bid)*(P(You get the property with Bid))

Profit = ($16,000 - 12800)*((12800 - $9,600)/($15,200 - $9,600) = $1828.57

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