國立中興大學教學大綱

課程名稱	(中) 機率(2355)
	(Eng.) Probability
開課單位	電資學士
課程類別	必修	學分	3	授課教師	許舜斌
選課單位	電資學士 / 學士班	授課使用語言	中文	英文/EMI		開課學期	1121
課程簡述	This course introduces the fundamental concepts of probability theory and its applications. Probability is the mathematical framework for modeling uncertainty and making informed decisions in a wide range of fields, including statistics, finance, engineering, and the natural sciences. The course will cover the following topics: Basic Probability Concepts: Sample spaces, events, probability axioms, complement rule, addition rule, conditional probability. Discrete Probability Distributions: Probability mass functions, cumulative distribution functions, expected value, variance, common discrete distributions (e.g., Bernoulli, Binomial, Poisson). Continuous Probability Distributions: Probability density functions, cumulative distribution functions, expected value, variance, common continuous distributions (e.g., uniform, normal, exponential). Joint Probability Distributions: Joint PMFs and PDFs, marginal and conditional distributions, independence. Transformations of Random Variables: Functions of random variables, distribution of sums and differences. Law of Large Numbers and Central Limit Theorem: Convergence in probability, weak law of large numbers, central limit theorem. Statistical Applications: Probability in statistical inference, hypothesis testing, confidence intervals. Simulation and Monte Carlo Methods: Using random numbers to solve practical problems. Prerequisites: This course typically requires a solid foundation in basic algebra and mathematical reasoning. Some courses may have additional prerequisites in calculus.
先修課程名稱						課程含自主學習	N

課程與核心能力關聯配比(%)

課程目標之教學方法與評量方法

課程目標

核心能力

配比(%)

教學方法

評量方法

1. Develop a Solid Understanding of Probability Concepts;
2. Apply Probability Theory to Real-world Situations;
3. Master Discrete and Continuous Probability Distributions;
4. Understand Joint and Conditional Probability;
5. Explore Independence and Dependence of Events;
6. Learn Transformations of Random Variables;
7. Apply the Central Limit Theorem;
8. Utilize Simulation and Monte Carlo Methods;
9. Apply Probability in Statistical Inference;
10.Develop Strong Mathematical Reasoning and Problem-Solving Skills;
11.Communicate Results Effectively;
12.Apply Probability Concepts in Multidisciplinary Contexts;

網路/遠距教學

習作

討論

講授

測驗

授課內容(單元名稱與內容、習作/每週授課、考試進度-共18週)

週次	授課內容
第1週	Combinatorial Analysis (I)
第2週	Combinatorial Analysis(II)
第3週	Axioms of Probability
第4週	Conditional Probability and Independence (I)
第5週	Conditional Probability and Independence (II)
第6週	Definition of Random Variables
第7週	Expectation of Discrete Random Variables
第8週	Discrete Probability Distributions
第9週	Midterm exam.
第10週	Continuous Probability Distributions
第11週	Jointly Distributed Random Variables
第12週	Properties of Expectation
第13週	Variance, Covariance and Correlation
第14週	Moment Generating Functions
第15週	Inequalities & Weak Law of Large Number
第16週	Central Limit Theorem
第17週	Strong Law of Large Number
第18週	Final exam.

學習評量方式

Quiz 40%
Midterm Exam 30%
Final Exam 30%

教科書＆參考書目(書名、作者、書局、代理商、說明)

A First Course in Probability, 9th edition, by Sheldon Ross
Pearson Education, Inc.(book agent in Taiwan (TEL) 04-2241-3551)

課程教材（教師個人網址請列在本校內之網址）

https://sites.google.com/view/signals-system-engineering-lab/course-info/probability

課程輔導時間

Thu. 10am-12pm

聯合國全球永續發展目標

提供體驗課程：N

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更新日期西元年/月/日：2023/10/15 15:31:57	列印日期西元年/月/日：2024 / 5 / 09
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