Suppose we are interested in bidding on a piece of land and we know one other bi

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 $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,500.

Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?

What amount should you bid to maximize the probability that you get the property (in dollars)?

Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,200. If your objective is to maximize the expected profit, what is your bid?
SelectStay with your bid in part (c); it maximizes expected profitBid $13200 to maximize the expected profitItem 4

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

Explanation / Answer

Ans:

Cumulative distribution function:

P(X<=x)=(x-10400)/(15500-10400)=(x-10400)/5100

a)P(X<=12000)=(12000-10400)/5100=0.3137

b)P(x<=14000)=(14000-10400)/5100=0.7059

c)Maximum pobability is 1 to get property,so bid 15501

d)

Expected profit = (16,000 - Bid)*(P(You get the property with Bid))

= (16,000 - 13200)*((13200-10400)/(15,500 - 10400))

=2800*0.549

=1537.2

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