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 $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? If required, round your answer to two decimal places.
(b) Suppose you bid $14,000. What is the probability that your bid will be accepted? If required, round your answer to two decimal places.
(c) What amount should you bid to maximize the probability that you get the property?

Answer 1

Step-by-step explanation:

f(x) = (1/(15,000-10,000))/0 (elsewhere) = 1/5000

a. What is the probability that a $12,000 bid will be accepted?

P(10,000 < x < 12,000) = 2000(1/5000) = 0.40

b. What is the probability that a $14,000 bid will be accepted?

P(10,000 < x < 14,000) = 4000(1/5000) = 0.80

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

$14,000 is my answer.

$14000 bid has a higher probability, hence a greater chance of being accepted