首頁 > 線上測驗 > 100年研究所工程數學歷屆試題(工數1)電機所.電子所. 電信所.光電所.通訊所(二年期) > 100年國立台北科技大學電腦與通訊所甲組工程數學
Given a system Ax = b , where
Find the value of a that makes the given system inconsistent.
Determine the least squares solution to Ax = b , where
Let
(1) Find the eigenvalues of A and the corresponding eigenvectors.
(2) Is matrix A diagonalizable? That is, can we find a nonsingular matrix S and a
diagonal matrix D such that S−1AS = D ? If the answer is “Yes”, find the
resulted diagonal matrix D and the nonsingular matrix S that diagonalizes A .
On the other hand, give the reason if your answer is “No”.
The joint probability density function (p.d.f.) of the two random variables X and Y
is given by
(1) Find the constant c.
(2) Find the marginal p.d.f. of X and Y , i.e., to find fx(x) and fy(y) .
(3) Are the two random variables X and Y independent? Prove your answer.
(4) Find the mean and variance of X.
Consider the game of throwing a fair dice five times. Find the following probabilities.
(1) The probability that the sixth-point occurs three times during the five trials.
(2) The sixth-point occurs one time in the first trial given that the sixth-point occurs
three times during the five trials.
Let X be a random variable that denotes the score of students in the subject
“Engineering Mathematics”. It is known that X has a mean E[X] = μ = 40 and
variance σ2 = 4 . Determine the two parameters a and b , such that the mean and
variance after the linear transformation (aX + b) mare 60 and 16, respectively.
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