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研究所、轉學考(插大)◆統計學題庫 下載題庫

110 年 - 110 國立高雄大學_碩士班招生考試_金融管理學系:統計學#102158 

選擇:0題,非選:13題 我要補題 回報試卷錯誤
【非選題】
1.

1. Given n observed data points, say  6167d9062cbd6.jpg for i = 1,2,3,..., n , please answer the following questions:


【題組】

(1). (10%) Please show that the straight line best fits the points is6167d9226812e.jpg , where
6167d928134d1.jpg



【非選題】
2.【題組】

(2). (3%) Given five observed data points in Table 1:   6167d951decf7.jpg Please use the results of (1) to find the least-squares line (regression line). 



【非選題】
3.【題組】

(3). (5%) Please evaluate the coefficient of determination 6167d9734fbcd.jpg



【非選題】
4.

2. Let 6167d98fe262a.jpg, for i = 1, 2,3,... , be independent and identically distributed (i.i.d.) random variables. The expectation and variance of each 6167d996445a5.jpg are μ and σ2 , respectively. Please answer the following questions:


【題組】

(1). (5%) What is the probability distribution of 6167d9d09dad5.jpg?



【非選題】
5.【題組】

(2). (10%) Let x1 , x2 , x3 , …, xm be m samples of a random variable X . If m is sufficiently large ( m  30 ), please show that the 95% confidence interval for the mean of X is:
6167d9eab328a.jpg
 where 6167d9ff3d646.jpg and 6167da0539b50.jpg denote the sample mean and sample standard deviation, respectively.



【非選題】
6.3. (10%) A teacher believes that the average grade of a class of 100 students is not higher than 85. The teacher randomly selects 64 students. The average grade of the 64 students is 87.8 and the standard deviation is 12.8. Using a significance level of 0.05, what conclusion should the teacher make?

【非選題】
7.

4. (5%) Let 6167da2849d12.jpg and Var ( X ) denote the expectation and variance of a random variable X , respectively. Please show that
6167da3b0f8a1.jpg



【非選題】
8.

5. Let X be normally distributed with mean 0 and variance 1. The probability density function of X is 6167da570e166.jpg . Please answer the following question:


【題組】

(1). (7%) What is the probability density function of 6167da6a7f6cf.jpg , where μ and σ>0 are constant?



【非選題】
9.【題組】(2). (7%) What is the probability density function of X2 ?

【非選題】
10.

≤≤≤≤6. Let N(t) , where 0 ≤ t ≤ T , denote a stochastic process, which satisfies the following conditions:
i. N (0)= 0 .
ii. N (t2)- N (t1) is normally distributed with mean 0 and variance t2 - t1 , where
0 ≤ t1 < t2 ≤ T .

iii. N(t) has independent increments. That is, given 6167db5de57a9.jpg

6167db6b8ff09.jpg are mutually independent.
Please answer the following question:


【題組】 (1). (7%) Please evaluate the expectation of N(s)N(t) , where 0≤ s < t ≤ T . ( Hint: N(t)-N(s))+N(s)-N(0)))


【非選題】
11.【題組】

(2). (7%) Please show that the correlation coefficient between N(s) and N(t) is6167dc421989d.jpg , where 0≤ s < t ≤ T .



【非選題】
12.【題組】

(3). (12%) Let 6167dc6e11337.jpg denote the price of a stock, where S ( 0 )= 10 is the share price at t = 0 . What is the expected share price at t = T ? That is, please evaluate the expectation of S(T) . ( Hint: N(t)=N(t)-N(0) is normally distributed.) 



【非選題】
13.【題組】

(4). (12%) Let X =6167dcd4990ee.jpg . Please show that the expectation of X is
6167dce19c4e8.jpg You may begin with finding the minimum value of N(1) such that S(1)≥ 10 .



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圖(一)、圖(二)、圖(三)顯示為三個對外國開放通商港口的階段。試回答第38-40題: 【題組】38.(  ) 由圖(一)演變至圖(二)是受到那個條約的影響...

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110 年 - 110 國立高雄大學_碩士班招生考試_金融管理學系:統計學#102158-阿摩線上測驗

110 年 - 110 國立高雄大學_碩士班招生考試_金融管理學系:統計學#102158