# Question: A consultant knows that it will cost him 10 000 to

A consultant knows that it will cost him $10,000 to fulfill a particular contract. The contract is to be put out for bids, and he believes that the lowest bid, excluding his own, can be represented by a distribution that is uniform between $8,000 and $20,000. Therefore, if the random variable X denotes the lowest of all other bids (in thousands of dollars), its probability density function is as follows:

a. What is the probability that the lowest of the other bids will be less than the consultant's cost estimate of $10,000?

b. If the consultant submits a bid of $12,000, what is the probability that he will secure the contract?

c. The consultant decides to submit a bid of $12,000.

What is his expected profit from this strategy?

d. If the consultant wants to submit a bid so that his expected profit is as high as possible, discuss how he should go about making this choice.

a. What is the probability that the lowest of the other bids will be less than the consultant's cost estimate of $10,000?

b. If the consultant submits a bid of $12,000, what is the probability that he will secure the contract?

c. The consultant decides to submit a bid of $12,000.

What is his expected profit from this strategy?

d. If the consultant wants to submit a bid so that his expected profit is as high as possible, discuss how he should go about making this choice.

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