E4070 教學大綱表

教學大綱表 (113學年度第1學期)

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課程名稱 Course Title	(中文) 隨機過程 (英文) Random Variable & Stochastic Process			開課單位 Departments	電機工程學系
				課程代碼 Course No.	E4070
授課教師 Instructor	龔宗鈞
學分數 Credit	3.0	必/選修 core required/optional	選修	開課年級 Level	大四
先修科目或先備能力(Course Pre-requisites)：工程數學(微積分、矩陣、富氏分析)
課程概述與目標(Course Overview and Goals)：使學生了解隨機變數與隨機過程之數學理論與物理觀念，並能夠應用於系統上之分析與設計。
教科書(Textbook)	作者 : Peyton Z. Peebles, Jr. 書名 : Probability, Random Variables and Random Signal Principles 出版社 : McGraw Hill(ISBN 0-07-118181-4)
參考教材(Reference)

課程大綱 Syllabus			學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
序 No.	單元主題 Unit topic	內容綱要 Content summary	學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
1	Introduction	1. Random variables 2. Random process	To understand: the concept of random variables and random process.	講授
2	The Random Variable	1. The Random Variable Concept 2. Distribution Function 3. Density Function	To understand: definition of random variable, conditions for a function to be a random variable, discrete and continuous random variable, mixed random variable, distribution function, density function.	講授
3	The Random Variable	1. The Gaussian Random Variable 2. Other Distribution and Density Examples 3. Conditional Distribution and Density Function	To understand: definition of Gaussian random variable, other distribution and density examples, conditional distribution function, density function.	講授	作業	HW 1
4	Operations on One Random Variable (RV)	1. Expection 2. Moments	To understand: expected value of a RV, expected value of a function of a RV, moments about the origin, central moments, variance and skew, Chebychev's inequality.	講授
5	Operations on One Random Variable (RV)	1. Transformations of a Random Variable	To understand: monotonic transformations of a continuous RV, nonmonotonic transformations of a continuous RV, transformation of a discrete RV.	講授	作業	HW 2
6	Multiple Random Variables	1. Vector Random Variables 2. Joint Distribution and Its Properties 3. Conditional Distribution and Density	To understand: joint distribution function and its properties, marginal distribution functions, conditional distribution and density.	講授	平時考	Quiz 1
7	Multiple Random Variables	1. Statistical Independence 2. Distribution and Density of a Sum of RVs 3. Central Limit Theorem	To understand: statistical independence of RVs, distribution and density of a sum sum of two RVs, central limit theorem.	講授
8	期中考	筆試	課程複習及筆試		期中考
9	Operations on Multiple Random Variables	1. Expected Value of a Function of Random Variables 2. Joint Characteristic Functions 3. Joint Gaussian Random Variables	To understand: joint moments about the origin, joint characteristic functions, joint Gaussian RVs.	講授
10	Random Processes-Temporal Characteristics	1. The Random Process Concept 2. Stationarity and Independence	To understand: classification of processes, statistical independence, first-order stationary process, second-order and wide-sense stationarity, N-order and strict-sense stationarity, time average and ergodicity.	講授
11	Random Processes-Temporal Characteristics	1. Correlation Functions 2. Measurement of Correlation Functions	To understand: autocorrelation function and its properties, cross-correlation function and its properties, covariance functions.	講授	作業	HW 3
12	Random Processes-Temporal Characteristics	1. Gaussian Random Processes 2. Poisson Random Processes	To understand: the properties of Gaussian random processes, Poisson random processes	講授	平時考	Quiz 2
13	Random Processes-Spectral Characteristics	Power Density Spectrum and Its Properties	To understand: the power density spectrum and its properties, bandwidth of the power density spectrum.	講授
14	Random Processes-Spectral Characteristics	Relationship between Power Spectrum and Autocorrelation Function	To understand: relationship between power spectrum and autocorrelation function.	講授	作業	HW 4
15	Random Processes-Spectral Characteristics	Cross-Power Density Spectrum and Its Properties	To understand: the cross-power density spectrum and its properties.	演講	平時考	Quiz 3
16	期末考	筆試	課程複習及筆試		期末考
17	Linear Systems with Random Inputs	1. Linear System Fundamentals 2. Random Signal Response of Linear System	To understand: mean and mean-squared value of system response, autocorrelation function of response, cross-correlation functions of input and output.		彈性教學
18	Linear Systems with Random Inputs	Spectral Characteristics of System Response	To understand: power density spectrums of response, cross-power density spectrums of input and output.	講授	彈性教學	HW 5 請於 2025/1/8 前於 Tronclass 繳交彈性教學週之作業HW5

彈性教學週活動規劃

序 No.	實施期間 Period	實施方式 Content	教學說明 Teaching instructions	彈性教學評量方式 Evaluation	備註 Notes
1	起:2024-01-02 迄:2024-01-05	1.同步遠距教學 Synchronous distance learning	1. Linear System Fundamentals 2. Random Signal Response of Linear System
2	起:2024-01-08 迄:2024-01-12	1.同步遠距教學 Synchronous distance learning	Spectral Characteristics of System Response	作業	請於 2024/1/12 前於 Tronclass 繳交彈性教學週之作業 HW 5

教學要點概述：
1.自編教材 Handout by Instructor：
□ 1-1.簡報 Slids
□ 1-2.影音教材 Videos
□ 1-3.教具 Teaching Aids
■ 1-4.教科書 Textbook
■ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

成績考核 Performance Evaluation：期末考：30% 期中考：30% 彈性教學：10% 平時考：20% 作業：10%

教學資源(Teaching Resources)：
■ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php