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 $9,800 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,800 and $14,700. 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)? 1 What amount should you bid to maximize the probability that you get the property (in dollars)? tho amount shown in

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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### Bidding on a Piece of Land: Probabilities and Strategy

Suppose we are interested in bidding on a piece of land, knowing that one other bidder is also interested. The seller has announced that the highest bid exceeding $9,800 will be accepted. Assume the competitor's bid, \( x \), is a random variable uniformly distributed between $9,800 and $14,700.

- **Scenario 1**: Suppose you bid $12,000. What is the probability that your bid will be accepted? (Round to 2 decimal places)
  - [Input Box]

- **Scenario 2**: Suppose you bid $14,000. What is the probability that your bid will be accepted? (Round to 2 decimal places)
  - [Input Box]

- **Optimal Bid Strategy**: What amount should you bid to maximize the probability of obtaining the property? (Provide the amount in dollars)
  - [Input Box]

- **Profit Maximization**: Suppose you know someone is willing to pay you $16,000 for the property. You are considering the bid from part (c), but a friend suggests you bid $12,900. If your goal is to maximize expected profit, what should your bid be?
  - [Dropdown Selection]

- **Expected Profit Calculation**: What is the expected profit for this bid (in dollars)?
  - [Input Box] 

Explore these scenarios and input your answers to determine the best bidding strategy and expected outcomes.
Transcribed Image Text:### Bidding on a Piece of Land: Probabilities and Strategy Suppose we are interested in bidding on a piece of land, knowing that one other bidder is also interested. The seller has announced that the highest bid exceeding $9,800 will be accepted. Assume the competitor's bid, \( x \), is a random variable uniformly distributed between $9,800 and $14,700. - **Scenario 1**: Suppose you bid $12,000. What is the probability that your bid will be accepted? (Round to 2 decimal places) - [Input Box] - **Scenario 2**: Suppose you bid $14,000. What is the probability that your bid will be accepted? (Round to 2 decimal places) - [Input Box] - **Optimal Bid Strategy**: What amount should you bid to maximize the probability of obtaining the property? (Provide the amount in dollars) - [Input Box] - **Profit Maximization**: Suppose you know someone is willing to pay you $16,000 for the property. You are considering the bid from part (c), but a friend suggests you bid $12,900. If your goal is to maximize expected profit, what should your bid be? - [Dropdown Selection] - **Expected Profit Calculation**: What is the expected profit for this bid (in dollars)? - [Input Box] Explore these scenarios and input your answers to determine the best bidding strategy and expected outcomes.
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