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義守大學 93 學年度博士班入學招生考試試題 系所別 工業工程與管理學系 考試日期 93/07/03 考試科目 高等統計學 總頁數 1 ※ 此為試題卷，考生請於答案卷上作答。 ※ 本考科不可使用計算機、不可使用字典。 1. Find the maximum likelihood estimator of θ for f ( x | θ ) = θe −θx , x>0, based on a random sample of size n. (20%) 2. If the percentage of defective parts turned out by a workman during two consecutive weeks was 7 and 9 percent, respectively, and if 500 parts were turned out during each of these weeks, would the inspector be justified in claiming that quality had slipped? (15%) 3. If X and Y are independent random variables, show that the curve of regression, if it exists, will be a horizontal straight line. What is the equation of the line? (15%) 4. Derive the least squares equations for fitting a curve of the type y = ax + to a set of n points in the x, y plane. (20%) 5. In the two-factor factorial design, (a) Please show that SST=SSA+SSB+SSAB+SSE. (20%) (b) Construct the ANOVA table. (10%) 第1頁 b x