題組內容

3. A consultant knows that it will cost her $10,000 to fulfil a particular contract. The contract is to be put out for bids, and she believes that the lowest bid, excluding her 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 $$f_x(x) = \begin{cases} \frac{1}{12}, & \text{for } 8 < x < 20 \\ 0, & \text{for all other values of } x \end{cases}$$

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