Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seliler announced that the highest bid in excess of s9,700 l be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,700 and $14,700 bid $12,000. What is the probability that your bid will be accepted (to 2 decimals) b. Suppose you bid s14,000, What is the probability that your bid will be accepted (to 2 decimals)? c. What amsunt should you bis to maximine the probability that you get the preperty? e that you know someone is wing to pay yo」$16,000 for the property. You are considering bidding the amount shown in part e but , triend suggests you be s12 ssa r your eb ective is t maximize the expected pront, what is your bi? what is the expected profit for this bid (to 2 decimals)?

Answer 1

6.7)

a) probability=(12000-9700)/(14700-9700)=0.46

b)

probability=(14000-9700)/(14700-9700)=0.86

c)

amount =14700

d)

bid =(16000-9700)/2+9700=12850

expected profit =(16000-12850)*(12850-9700)/(14700-9700)=1984.50

2)

a) z =-0.82

b) z =1.68

c)z =0.28

d)z=2.58

e)z =-0.51