世新大學九十三學年度碩博士班考試試題卷
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學 系 別 |
考 試 科 目 |
|
財務金融學系 |
統計學 |
※考生請於答案卷內作答
Part A 填充題：請順序填寫答案，標明題號，不需列出計算過程。共55分
I. Two players, A and B, alternatively and independently flip a coin, with probability 1/3 obtain a head. The rule is that the first player to obtain a head wins. Who will flip first is decide by flipping another coin, with probability 2/3 to obtain a head; if the outcome is head, then A flips first, otherwise, B flips first. What is the probability that A wins ? (1) (10%)
II. Consider the regression model 
where 
’s are iid 
. The regression equation 
is obtained.
After algebra, results are as follows : 
,
(a)
R2= (2)
(5%)
(b) Provide a test statistics value (3) for testing H0:a0 =1. (5%)
(c) Provide a test statistics value (4) for testing H0:a2-a1=1. (5%)
III. The joint pmf is given as follows:
X=1 X=2 X=3
------------------------------------------------------------
Y=0 0.10 0.05 0.10
Y=1 0.15 0.20 0.10
Y=2 0.05 0.15 0.10
--------------------------------------------------------------
(a) Find the conditional expectation
function 
(5) (5%)
(b) Find the covariance between X and Y, Cov(X,Y) =(6) (5%)
(c) Find the correlation coefficient between X and Y, 
=(7) (5%)
IV. 設X1,X2,…,Xn為一組來自常態
母體之隨機樣本。令
及
分別為
及
之MLE。則=(8) ，之抽樣分配為(9) ，
之抽樣分配為(10) (15%)
Part B 計算題：請順序答題，計算過程擇重點列出，共45分
I 台灣股市大盤自1991年至2000年，其第一季(X )及第三季(Y)之各季季報酬如下：
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|
第一季 第三季 |
|
第一季 第三季 |
|
1991年 1992年 1993年 1994年 1995年 |
0.24 -0.13 0.01 -0.20 0.43 -0.03 -0.17 0.19 -0.07 -0.05 |
1996年 1997年 1998年 1999年 2000年 |
-0.00 0.00 0.20 -0.03 0.11 -0.14 0.14 -0.10 0.15 -0.27 |
設各季之季報酬率互相獨立，分別是為從兩個常態母體
及
所隨機抽取之樣本。而且
。
(a)試檢定
對
。
(10%)
(b)試檢定
對
。
(10%)
II. There suppliers provide the following data on defective parts：
Part Quality
|
Supplier |
Good |
Minor Defective |
Major Defective |
|
A B C |
90 180 160 |
3 8 19 |
7 12 21 |
Use 
=0.05 and test for independence between supplier and part
quality. What dose result of your analysis tell the
purchasing department?
(15%)
III. X and Y are two random variables, such that both 
and 
exist,
(a)
Show that
.
(5%)
(b)
Show that 
(5%)
-----The end ------
Tables
|
|
|
df |
8 |
9 |
10 |
18 |
19 |
20 |
|
|
|
a |
1.860 |
1.833 |
1.815 |
1.734 |
1.729 |
1.725 |
|
|
a |
2.306 |
2.262 |
2.228 |
2.101 |
2.093 |
2.086 |
|
|
df |
1 |
2 |
3 |
4 |
5 |
6 |
|
a |
3.84 |
5.99 |
7.81 |
9.49 |
11.07 |
12.59 |
|
|
(m,n) |
(8,8) |
(9,9) |
(10,10) |
|
(m,n) |
(8,8) |
(9,9) |
(10,10) |
|
|
3.44 |
3.18 |
2.98 |
|
4.43 |
4.03 |
3.72 |