Q1.(10%) Consider two events A and B, prove that if A and B are independent, then so are .

(2)請試著說明，這場危機介入的主要目標為何？（3 分）

(3)請列出危機介入的具體步驟，並說明你會如何進行？（15 分）

3.校園自殺防治計畫，通常會將所有教職員均納入計畫當中。而自殺防治守門人訓練中所指的一問、二應、三轉介，所指意義 為何？（10 分）校園危機輔導工作，在發展性、介入性、處遇性三個層級，大致包括哪些工作內容？（15 分）

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10% by rural areas. Of the municipal bonds rated B, 60% were issued by cities, 20% by suburbs, and 20% by rural arcas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs, and 5% by rural areas. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? 

Three events: A1, A2 and B are given. We know that A1 and A2 are disjointed events. P(A1)>0 and P(A2)>0. Let P(B|A1)= P(B|A2)=0.2. Please find P(B|A1UA2).

(a) (3%) Find the eigenvalues of A. ul

(b) (6%) Is A diagonalizable? Justify your answer.

107台大資工 (10%) Your answer will be considered correct only if all the true statements are selected. Let A be an nxn matrix. (a) If x1 and x2are the cigenvectors of A, then x1 + x2 is also an eigenvector of A. (b) If AT = -A, then A is singular. (c) If A2 = A. (A+1)n = 1 + (2n+1)A. (d) If A = AT, then A is diagonalizable.(e) If A = and B and D are invertible,then.

110交大資訊聯招 b.(10 points) Given a sequence 7, -6, 20, -24, 64, -96,... comes from for k ≥ 0, with G0 = 7, G1 = -6 and G2 = 20. Please find the number .

(a) (4%) What are the values of G4 and G5?