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 $14,500.
a. Suppose you bid $12,000. What is the probability that your bid will be accepted?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
c. What amount should you bid to maximize the probability that you get the property?
d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

Answer:

0.4185;

0.8835;

$14500;

No

Step-by-step explanation:

Given that :

a = 10200

b = 14500

f(y) = 1 /(b - a) = 1/(14500 - 10200) = 1/4300 = 0.0002325

A.)

P(x <12000) = ∫fydy at(12000 ; 10200) = ∫0.0002325dy at(12000 ; 10200)

P(x < 12000) = 0.0002325(12000) - 0.0002325(10200) = 0.4185

B.)

P(x <14000) = ∫fydy at(14000 ; 10200) = ∫0.0002325dy at(14000 ; 10200)

P(x < 14000) = 0.0002325(14000) - 0.0002325(10200) = 0.8835

(c.) 14500 ; because competitor's bid is at most 14500

D.) No ; Because by bidding $14500 ; getting the property is certain ; once the property is gotten, then it could be resold for $16000, to make a profit of $1500 ; by bidding less, winning the bid becomes uncertain which may means the profit might be lost in the long run.

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