Suppose we are interested in bidding on undeveloped land in Nevada and reselling
ID: 3222005 • Letter: S
Question
Suppose we are interested in bidding on undeveloped land in Nevada and reselling it for a profit to unsuspecting californians for $16,000. If e know that one other bidder is the only competition and he never bids more than $15,000, what would you bid to maximize the probability you win.
A. If the minimum bid must be $10,000 and our competitor's strategy follows a uniform distribution, draw the probability distribution of his bids.
B. Find the probability that you get the land if you bid $14000. That is: compute the probability the competitor bids less than $14,000
C. Find the bid that maximizes your profit over time if you incur an additional cost of $100 when you don't get the bid. What is your expected profit? Define expected value!
Explanation / Answer
a) Given Resale amount = $ 16,000
Other bidder amount limit (not more than )= $15,000
The minimum bid =$10,000
The probability density function of X:
P(X=x) =1/(b-a) , (a x b)
P(X=x) = 1/(16000-10000) =1/6000 , (10000 x 16000)
The cumulative distribution of the function of X:
P(X x) = (x –a) / (b-a) , (10000 x 16000)
=( x-10000) /6000 , (10000 x 16000)
b) The probability the competitor bids less than $14,000
P(X < 14000) =( x-10000) /6000
=(14000-10000)/6000
= 0.6666
= 0.7
c) Expected value E(X) = (a+b) /2
=(10000+16000) /2
=26000/2
= 13000
Additional cost on bid is $100
The expected profit for this bid is =13000 + 100 =$13100
Expected value :a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence
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