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  1. #1
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    probability




    I just posted another question and figured it out by myself but now i'm really stuck. Any suggestions to help me through it? Any input would be helpful.

    Thanks,
    Corey

    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 $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,500.


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



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



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



    d.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 $13,000. If your objective is to maximize the expected profit, what is your bid?
    SelectStay with your bid in part (c); it maximizes expected profitBid $13,000 to maximize the expected profitItem 4

    What is the expected profit for this bid (in dollars)?
    Last edited by USMstudent85; 04-11-2011 at 10:41 AM.

  2. #2
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    Re: probability

    So I just figured out A-C.

    A) 2000(1/5500)=.36
    B) 4000(1/5500)=.73
    C)$15500

    Need help with D. Please any suggestions.

    d.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 $13,000. If your objective is to maximize the expected profit, what is your bid?
    SelectStay with your bid in part (c); it maximizes expected profitBid $13,000 to maximize the expected profitItem 4

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

    I need the question in bold. Please help.

  3. #3
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    Re: probability

    The teacher posted this for us to use on this problem. Im still not getting the answer. Any suggestions?

    Round f(x) to six decimals.

    d) Do the following for both your bid from part c and your friend's suggested bid:

    Compute the initial profit using the following: amount paid to you - bid
    Compute the expected profit using: initial profit * probability of winning with that bid
    Compare your results.

  4. #4
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    Re: probability


    For example, if you bid $12,000: then profit = $4,000 and P(profit) = 0.36. The other 64% of the time you will have no profit. So expected profit = $1440.

    If you bid $15,000: then profit = $1,000 and P(profit)=0.73. So expected profit = $730.


    If you bid X: then profit = (16000-X) and P(profit) = \frac{X-10000}{5500}. So expected profit = ..., and you want to find X to maximize that.

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