(a) Find A such that this is a proper p.d.f. (b) Find the probability that 0 <x < 0.4 and 0.6 < y < 1 參考解答 (c) Obtain the marginal p.d.f.’s for X and Y.
2.Many companies must accurately estimate their costs before a job is begun in order to acquire a contract and make a profit. For example, a beating and plumbing contractor may estimate costs for new homes based on the total area of the house and whether central air conditioning is to be installed. (25%) (a) Write a main effects model relating the mean cost of material and labor, E(y), to the area and central-air-conditioning variables. (b) Write a complete second-order model for the mean cost as a function of the same two variables. (c) The contractor samples 25 recent jobs, fitting both the complete second-order model (part b) and the reduced main effects model (part a), so that a test can he conducted to determine whether the additional complexity of the second-order model is necessary. The resulting SSB and values are shown in the table below. Is there sufficient evidence to conclude that the second-order terms are important for predicting the mean cost? Use a= 0.05. (There is no probability table available, please write in more detail.)
SSE
Main effects
8.548
0.950
Second-order
6.133
0.964
3. Samantha was a student at University of Wisconsin - Stout majoring in Accounting. In the summer after her sophomore year she got an intern job at the First National Bank. As her boss, Brad, assumed that she must have taken statistics course in the business school, he asked Samantha to give him a 95% interval estimate of the average amount of money their customers opened a certificate deposit with the bank. Samantha randomly selected 5 from all the certificate deposits currently valid with them and found the principals were $5,800, $6,000, $5,300, $8,100, and 7,300. Samantha gave an interval estimate of between $5,292 to $7,708. Was she correct? If not, what do you think a correct interval would be? (16 %) 參考解答
4. The manager of an auditorium where pop concerts are often held has found that the attendance to this kind of concert is normally distributed with an average of 6,000 people, and standard deviation 1,500. The tickets are sold at a flat rate of $500 each. Overall, all concert organizers who rent this auditorium lose money on 20% of time. For the upcoming concert, how many people the concert must draw in order for the concert organizer to break even? (17%) 參考解答
5. Suppose the three most favorite kinds of food ordered at local McDonald’s stores were Big Mac, French Fries, and Chicken McNuggets. To focus on those 3 kinds of food, all the customers who ordered any single selections or combinations of the three selections were called the MFM segment. A staff with an MBA degree was called to do an analysis. She reported to the COO, “Based on our internal records, 43.6% of our MFM customers ordered Big Mac, 52% bought French Fries, and 30% ate Chicken McNuggets.” Proudly she continued, “My analysis shows that 1 out of 10 MFM customers ordered Big Mac and French Fries, 15.6% ordered Chicken McNuggets and French Fries. And, surprisingly, none had Big Mac and Chicken McNuggets together,” The COO then asked a question, “What is the percentage of MFM customers who ordered either French Fries or Chicken McNugget alone?” A correct answer by the staff should be________%(17%) 參考解答
values are shown in the table below. Is there sufficient evidence to conclude that the second-order terms are 