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 $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $14,600.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 (in dollars)?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 $13,200. If your objective is to maximize the expected profit, what is your bid? (Options: 1. Stay with the bid in part (c) or 2. Bid $13,200 to maximize profit)What is the expected profit for this bid (in dollars)?

Answer 1

Answer:

a. 0.32

b. 0,72

c. $13200

d. No

Step-by-step explanation:

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 $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $14,600.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 (in dollars)?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 $13,200. If your objective is to maximize the expected profit, what is your bid? (Options: 1. Stay with the bid in part (c) or 2. Bid $13,200 to maximize profit)What is the expected profit for this bid (in dollars)?

a=10400

b=14600

probability density is gotten by inverse of difference in boundaries

$\frac{1}{14600-10400}$ =f(y)

0.0002

a. for probability x<12000$\int\limits^12000_10400 {f(y)} \, dy\\\int\limits^12000_10400 {0.0002} \, dy$

(0.0002) from 12000 to 10400

0.32

b. probability that y x<14000

integrate f(y)dy

between 14000 and 10400

0.0002x

0.72

c.

Bid at most 13200 to be sure that it will be at maximum

d. No, if the house is sold for 16000 you could make a profit of $2800, because the house is $13200. You will run at loss is you bid less