Math Help - 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 , then his probability of winning is:



Then his expected profit if he bids is:



Now you need to find the that maximises

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 long is the
proportion of lowest bids that are greater than . is converted into units of .

is the profit if you bid and so is , and is the expected
profit if you bid .

RonL

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