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題組內容

1 Let

be a random sample of size n. Using it, define the following; (18%)

(a) Sample mean

其他申論題

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

【已刪除】8. (10 points) Let v1 and v2 be eigenvectors of a linear transformation T ： V →V with corresponding eigenvalues λ1 and λ2 respectively. Prove that, and v2 are indepeudent(線性獨立).

9. (10 points) Let P and Q be n x n matrices. We say P is similar to Q if there exists an invertible n x n matrix C such that C-lPC = Q. Prove that similar square matrices have the same eigenvalues with the same algebraic imilUplickies(代數重根數)•

【已刪除】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 that A is an orthogonal matrix(正交矩陣).

(b) Sample median

(c) Sample mode

(d) Sample variance

(e) Sample standard deviation

(f) The coefficient of variation.

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

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