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 $10,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,500 and $15,200.

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) What is the expected profit for this bid (in dollars)?

Answer 1

for uniform distribution parameter:a =10500and b=15200

a)

a)probability that 12000 bid be accepted =P(X<12000)=(x-a)/(b-a)=(12000-10500)/(15200-10500)=

0.32

b)

a)probability that 14000 bid be accepted =P(X<14000)=(x-a)/(b-a)=(14000-10500)/(15200-10500)=

0.74

c)

maximum bid for max probability =b=

15200

D)

expected profit =(16000-13250)*(13250-10500)/(15200-10500)=

1609.04