Suppose we are interested in bidding on a piece of land and we know one other bi

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 $10,300 will accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,300 and $15,400. 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 $13,150. If your objective is to maximize the expected profit, what is your bid? Bid $ 13,150 to maximize the expected profit What is the expected profit for this bid (to 2 decimals)? $ 1201.0

Explanation / Answer

X ~ unif(10300,15400)

P(X <a) = (a-10300)/(15400-10300)    10300 < a< 15400

= (a -10300)/5100

a) P(X <12000) = (12000-10300)/5100 = 1700/5100 = 1/3 =0.3333

b) P(X < 14000) = 0.7254901

c) maximum when 15400 as x varies from 10000 and 15400,

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.