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Math Help - More Stats help!

  1. #1
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    Exclamation More Stats help!

    A contractor has found through experience that the low bid for a job (exclude his own bid) is a random variable that is uniformly distributed over the interval (0.75C, 2C) where C is the contractor's cost estimate (no profit or loss) of the job. If profit is defined as 0 if the contractor does not get the job (his bid id greater that the low bid) and as the difference between his bid cost estimate C, if he gets the job; what should he bid (in terms of C) to maximize his expected profit?

    Does anyone even understand where I would begin here or what time of way I would go about solving this???? THankssss again.
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  2. #2
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    Quote Originally Posted by Jar23 View Post
    A contractor has found through experience that the low bid for a job (exclude his own bid) is a random variable that is uniformly distributed over the interval (0.75C, 2C) where C is the contractor's cost estimate (no profit or loss) of the job. If profit is defined as 0 if the contractor does not get the job (his bid id greater that the low bid) and as the difference between his bid cost estimate C, if he gets the job; what should he bid (in terms of C) to maximize his expected profit?

    Does anyone even understand where I would begin here or what time of way I would go about solving this???? THankssss again.
    If the contractor bits b, then his probability of winning is:

     <br />
p(b) = \frac{2-b/c}{1.25} \ b \in [0.75c, 2c],\ 0 \mbox{ otherwise}<br />

    Then his expected profit if he bids b is:

     <br />
\bar{pr}(b)=(b-c)p(b)<br />

    Now you need to find the b that maximises \bar{pr}(b)

    RonL
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  3. #3
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    Exclamation

    Where did you get the p(b)= 2-b/c / 1.25??? Also where did you get the pr(b)??? Thanks so much!
    Last edited by Jar23; December 2nd 2007 at 10:33 AM.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jar23 View Post
    Where did you get the p(b)= 2-b/c / 1.25??? Also where did you get the pr(b)??? Thanks so much!

    You have a uniform distribution over an interval 1.25c long (2-(b/c))/1.25 is the
    proportion of lowest bids that are greater than b. (b/c) is b converted into units of c.

    pr(b) is the profit if you bid b and so is b-c, and \bar{pr}(b) is the expected
    profit if you bid b.

    RonL
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  5. #5
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    still not sure

    Still not sure what this about. Can you do this complete?
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