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 , x>0, based on a random sample of size n. (20%)
e x
x
f( |θ)=θ −θ
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
x ax b y= +
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%)
第 1 頁 (b) Construct the ANOVA table. (10%)
