2024 DSE 数学延伸部分-M1 真题 答案 详解

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真题(中文)

答案(英文)

2024 HKDSE Mathematics Extended Part (Module 1) Examination Suggested Solutions by Jacky Chan

0.3 + a + 0.1 + 0.2 + 0.2 = 1 a = 0.2

E(X) = 0 × 0.3 + 3 × 0.2 + 6 × 0.1 + b × 0.2 + 15 × 0.2 = 0.2b + 4.2

E(X^2) = 0^2 × 0.3 + 3^2 × 0.2 + 6^2 × 0.1 + b^2 × 0.2 + 15^2 × 0.2 = 0.2b^2 + 50.4

Var(5X) = 739 5^2 Var(X) = 739 Var(X) = 29.56

E(X^2) - [E(X)]^2 = 29.56 (0.2b^2 + 50.4) - (0.2b + 4.2)^2 = 29.56 0.16b^2 - 1.68b + 3.2 = 0 2b^2 - 21b + 40 = 0 (2b - 5)(b - 8) = 0 b = 5/2 (rej.) or 8

P(C) = 0.2 + 0.1 = 0.3

P(D) = 0.1 + 0.2 + 0.2 = 0.5

P(C ∩ D) = 0.1

P.1 (14) © Jacky Chan Yui Him (2024) All rights reserved.