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

科目：研究所、轉學考(插大)-應用數學 | 年份：110年 | 選擇題數：0 | 申論題數：22

試卷資訊

所屬科目：研究所、轉學考(插大)-應用數學

選擇題 (0)

申論題 (22)

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

(b) What is the normalization constant A such that ∫ Ap(x)da = 1? [3%]

(c) What is the corresponding mean for this distribution? [3%]

(d) What is the corresponding median for this distribution? [3%]

(e) What is the corresponding variance for this distribution? [4%]

(f) What is the corresponding skewness for this distribution? [4%]

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

(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)

(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%]

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

(b) If Y = Zab - c, where 2 is a constant, what is the expression of the error term for Y? [3%]

(c) IfY = a/b t e^c, 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,

, cannot be ignored.

(d) What is the expression of the error term for Y in (b)? [4%]

(a)f(z)=e^x-1.15%)

(b) f(a) = In(1 +x).[5%]

(c) f(z) = (1 + 2)ⁿ. [5%]

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

(b) The transpose of A, A^T. [3%]

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

(d) Symmetric matrix S and skew-symmetric matrix K such that A = S + K. [6%]

(e) Two eigenvalues of A. [5%]

(f) The corresponding two eigenvectors. [6%]