Thread: 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.

Originally Posted by Jar23

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 $\displaystyle b$, then his probability of winning is:

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

Then his expected profit if he bids $\displaystyle b$ is:

$\displaystyle
\bar{pr}(b)=(b-c)p(b)
$

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

RonL

Where did you get the p(b)= 2-b/c / 1.25??? Also where did you get the pr(b)??? Thanks so much!

Originally Posted by Jar23

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 $\displaystyle 1.25c$ long $\displaystyle (2-(b/c))/1.25$ is the
proportion of lowest bids that are greater than $\displaystyle b$. $\displaystyle (b/c)$ is $\displaystyle b$ converted into units of $\displaystyle c$.

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

RonL

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