教甄諮商輔導專業

【題組】(b)(5 points) Solve the linear system by Cramer’s rule.

7.【題組】(a)(10 points) Find the characterisLic polynomial(特徵多項式),the real eigenvalues(特 徵值）＞ and the c

【題組】(b)(5 points) Find an invertible matrix C and a diagonal matrix(對角矩陣）D such that D 二 C-MC.

8.(10 points) Let v1 and v2 be eigenvectors of a linear transformation T ： V →V with corresponding e

9.(10 points) Let P and Q be n x n matrices. We say P is similar to Q if there exists an invertible

10. (10 points) Let A be an n x n matrix such that Ax • Ay = x•y for all vectors x and y in. Show th

1Letbe a random sample of size n. Using it,define the following;(18%)【題組】(a)Sample mean

【題組】(b) Sample median

【題組】(c) Sample mode

【題組】(d) Sample variance

【題組】(e) Sample standard deviation

【題組】(f) The coefficient of variation.

2.(a) What is meant by "Events At B are mutually exclusive'' ? (2%)

(b)Letbe n mutually exclusive events such thatforj =1,2,...,n，and whose union is the entire sample s

(c)The Graduate Management Admission Test (GMAT) is a requirement for all applicants of MBA programs

【題組】(ii)Compute(6%)

【題組】(iii)Compute P(B). (4%)

【題組】(iv)Apply Bayes' Law Formula to compute(8%)

3(a) Let Z be a standard normal random variable. That is, Z 〜N(0，1).Let Fz be the distribution ftmct

(b) Let the random variable X have a Chi-Squared distribution with r degrees of freedom. What are th

4be a random sample of size n from a normal population with mean /i and known variance a2 ＞ 0 .【題組】(

【題組】(b)Give a confidence interval for μ with confidence coefficient a, 0 ＜ a ＜ 1 (6%)

5To lest the null hypothesis H0 against the alternative H1, by using a test.【題組】(a)What is a type I

【題組】(b)What is a type II error for this test? (4%)

【題組】(c)What is the power of this test?(4%)

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