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 $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,500. 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 $13,100. 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 profit or Bid $13,100 to maximize the expected profitItem

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

$ _______

c. the maximum bidder get the property, since the bid is in the range of $10100 and $14500, therefore, the bidder with $14500 or more will get the property.

d. if your objective is to maximize expected profit, stay with your bid in part c. which is $14500 or more will get the property.

e. the expected profit will be $14500 -$10100 = $4,400.00

Parrain Parrain · Answer 2 · 2025-03-23T21:00:55-04:00

Based on the variable being uniformly distributed, the Probability of $12,000 bid being accepted is 43.2%.

The probability of $14,000 bid being accepted is 88.6%.

The amount you should bid is $14,500.

The expected profit for the bid is is $1,972.

What is the probability that the bid of $12,000 is accepted?

= (Bid - lower range of uniform distribution) / (Upper range - Lower range)

= (12,000 - 10,100) / (14,500 - 10,100)

= 43.2%

What is the probability that the bid of $14,000 is accepted?

= (14,000 - 10,100) / (14,500 - 10,100)

= 88.6%

What amount should you bid to maximize your chances?

The amount you should bid that would maximize your chances should be the highest possible bid of $14,500.

What is the expected profit at this bid?

If you bid $13,100 and the person pays you $16,000, your profit would be:

= 16,000 - 13,100

= $2,900

The expected profit is therefore:

= Profit x Probability of winning by bidding 13,100

= 2,900 x ((13,100 - 10,100) / (14,500 - 10,100))

= 2,900 x 0.68

= $1,972

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