suppose we are interested in bidding one undeveloped land in Nevada and resellin
ID: 3248406 • Letter: S
Question
suppose we are interested in bidding one undeveloped land in Nevada and reselling it for a profit to unsuspecting Californians for $16000. If we know that one other bidder is the one 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 $10000 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 probablitiy the competitor bids less than $14000.
c) find the bid that maximizes your profit over time if you incur an additional cost of $100 when you dont get the bid. What is your expected profit? Define expected value.
Explanation / Answer
Solution:
We have Resale amount = $ 16,000
Other bidder amount limit (not more than ) = $15,000
a) 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
c) Expected value E(X) = (a+b) /2
=(10000+16000) /2
= 13000
The expected profit for this bid is =13000 + 100 =$13100
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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