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110 年 - 110 國立中央大學_碩士班招生考試_天文研究所:應用數學#110498 

選擇:0題,非選:22題 我要補題 回報試卷錯誤
【非選題】
1.
1. Variables a are uniformly distributed between interval a and b.

【題組】(a) What is the corresponding probability density function p(x)? [3%]


【非選題】
2.【題組】(b) What is the normalization constant A such that ∫ Ap(x)da = 1? [3%]

【非選題】
3.【題組】(c) What is the corresponding mean for this distribution? [3%]

【非選題】
4.【題組】(d) What is the corresponding median for this distribution? [3%]

【非選題】
5.【題組】(e) What is the corresponding variance for this distribution? [4%]

【非選題】
6.【題組】(f) What is the corresponding skewness for this distribution? [4%]

【非選題】
7.
2. Consider a linear regression in the form of y = ar +b with data points of (xi, yi), where i = 1,…,N.

【題組】 (a) Derive the analytical expression of slope a and intercept b. [14%]


【非選題】
8.【題組】(b) Calculate a and b for the following data points: (-2, -1), (1, 1) and (3, 2) [7%] (NOTE: you can express your answers as ratio instead of decimal number, for example 11/10 instead of 1.1)

【非選題】
9.【題組】(c) The data given in (b) can also be ftted with y = ar. Which regression, y = ax + b or y = ax, can ft the data better? Explain or argue your anwer. [7%]

【非選題】
10.

3. A measurement Y depends on variables (a,b,c), the standard deviation of these variables are known: (σa, σbc). Assume that the covariance terms can be ignored, answer the following:


【題組】

(a) What is the general equation for σY based on propagation of error? [2%]



【非選題】
11.【題組】(b) If Y = Zab - c, where 2 is a constant, what is the expression of the error term for Y? [3%]

【非選題】
12.【題組】(c) IfY = a/b t ec, where e is natural logarithm. What is the expression of the error term for y? [3%]
 Now assume that the covariance term for a and c, 63070c6500d23.jpg, cannot be ignored.


【非選題】
13.【題組】(d) What is the expression of the error term for Y in (b)? [4%]

【非選題】
14.
4. Write down the Taylor series expansion, up to first-order approximation, for the following function at 2 = 0.

【題組】(a)f(z)=ex-1.15%)


【非選題】
15.【題組】(b) f(a) = In(1 +x).[5%]

【非選題】
16.【題組】(c) f(z) = (1 + 2)n. [5%]

【非選題】
17.

5. Consider the following matrix:
  63070caed0bbc.jpg
Calculate or find out the following:


【題組】 (a) The determinant of A, det
(A). [2%]


【非選題】
18.【題組】(b) The transpose of A, AT. [3%]

【非選題】
19.【題組】

(c) The inverse of A, 63070cdb7680b.jpg. [3%]



【非選題】
20.【題組】(d) Symmetric matrix S and skew-symmetric matrix K such that A = S + K. [6%]

【非選題】
21.【題組】(e) Two eigenvalues of A. [5%]

【非選題】
22.【題組】(f) The corresponding two eigenvectors. [6%]

懸賞詳解

國二自然下第一次

29.( ) 實驗(一),碳酸鈣和鹽酸的反應。實驗(二):碳酸鈉和氯化鈣的反應。這兩個實驗皆在未加蓋的燒杯 內完成,水的蒸發不計。關於上述兩個實驗,下...

50 x

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110 年 - 110 國立中央大學_碩士班招生考試_天文研究所:應用數學#110498-阿摩線上測驗

110 年 - 110 國立中央大學_碩士班招生考試_天文研究所:應用數學#110498