   # Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. 1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between$10,000 and $15,000. a. Suppose you bid$12,000. What is the probability that your bid will be accepted? b. Suppose you bid $14,000. What is the probability that your bid will be accepted? c. What amount should you bid to maximize the probability that you get the property? d. Suppose you know someone who is willing to pay you$16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.1, Problem 7E
Textbook Problem
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## Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between$10,000 and $15,000. a. Suppose you bid$12,000. What is the probability that your bid will be accepted? b. Suppose you bid $14,000. What is the probability that your bid will be accepted? c. What amount should you bid to maximize the probability that you get the property? d. Suppose you know someone who is willing to pay you$16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

a.

To determine

Find the probability that a bid will be accepted for $12,000. ### Explanation of Solution Calculation: Two bidders are interested on a piece of land. The seller announced that the highest bid that is more than$10,000 will be accepted. The random variable x (competitor’s bid) follows uniform distribution between $10,000 and$15,000.

The probability density function for uniform distribution is,

f(x)={1bafor axb0  elsewhere

The probability density function for the competitor’s bid is,

f(x)={15,000for 10,000x15,0000          elsewhere

The cumulative density function for uniform distribution is,

P(xX)=Xaba

The bid will be accepted if the amount is more than $10,000 b. To determine Find the probability that the bid will be accepted for$14,000.

c.

To determine

Find the amount that maximizes the probability of bid to get the property.

d.

To determine

Explain that if anyone is interested to bid the property for $16,000, is this considered in bidding less than$15,000.

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