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 $10,200  will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,200 and $15,000. 

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)?  .79   

 
c. What amount should you bid to maximize the probability that you get the property?  $  15000   

 
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 $13,100. If your objective is to maximize the expected profit, what is your bid?   Bid $13100 to maximize the expected profit   
What is the expected profit for this bid (to 2 decimals)? 

I've already tried and got 1752.08 for the last question but that doesn't seem to be right.

Answer 1

ANS -- a) 19000 - 10200 15000 - 10200 1800 G 800 - 0.375 b) 14000 - 10200 15000 - 10200 3800 9800 0.7916. c) Well the probability of acceptance of my bid 6-10000 b= 15000. Which 4800 is intuitively clean too

6 16000-b if xab. Pb. o otherwise Fla) - (16000 - 6) P(x<6) POSE (C) Expected Profft E (P15000) - (16000-15000) :P (*< 150000) - 1000 I go with yny friend suggestion F (P13100) - (16000 – 13100) P (#543100) (2900) X 13100 - 10000 - 4800 = (2900 x 2900 (800 - 2900+ 0.6092 & 1752.18,