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 $9,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,500 and $15,500.
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 $12,750. If your objective is to maximize the expected profit, what is your bid?
SelectStay with your bid in part (c); it maximizes expected profitBid $12750 to maximize the expected profitItem 4
-What is the expected profit for this bid (in dollars)?

Answer 1

for uniform distribution parameter:a =9500and b=15100

a)

probability that 12000 bid be accepted =P(X<12000)=(x-a)/(b-a)=(12000-9500)/(15100-9500)=

0.45

b)

probability that 14000 bid be accepted =P(X<14000)=(x-a)/(b-a)=(14000-9500)/(15100-9500)=

0.80

c)

maximum bid for max probability =b=

15100

d)

if someone will ing to give you 16000; expected bid to get max profit=(16000-9500)/2+9500=

12750\

expected profit =(16000-12750)*(12750-9500)/(15100-9500)=

1886.16