課程資訊
課程名稱
 機率方法
Probabilistic Methods in Engineering 
開課學期
 110-1 
授課對象
 工學院  機械工程學系  
授課教師
 林以凡 
課號
 ME5057 
課程識別碼
 522EU6330 
班次
  
學分
 3.0 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期四7,8,9(14:20~17:20) 
上課地點
 工綜B03 
備註
 本課程以英語授課。
總人數上限：60人 
  
課程簡介影片
 
核心能力關聯
 本課程尚未建立核心能力關連
課程大綱
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課程概述

ME 5057 is an introductory probability and random process course for engineering students. Our syllabus has a strong emphasis on the theoretical foundations. ME 5057 is different from the statistics courses you took in high school. For example, you probably know about how to calculate the “mean” and “standard deviation” of some data, but have you thought about how to use the mean and standard deviation to classify objects in an image? We will not go deep into image classification in this course, but we will teach you a set of basic concepts in probability theory which will eventually allow you to study these problems in the future. 

課程目標
 The objective of this course is that by the end of the semester, you will have
• a solid background in probability and random processes that can help you take advanced courses;
• an ability to formulate engineering problems using a probabilistic approach;
• an ability to analyze large-scale systems using statistical methods;
• an ability to identify the concept of random variables and properties of common types of random variables, and how to solve probabilistic problems;
• experience in using computers to solve probability problems.
Also, you will be able to
• use set-theoretic notation to describe events and compute probabilities;
• compute and interpret conditional probability, total probability, and describe Bayes' theorem;
• test for independence of events or of random variables;
• describe different types of discrete random variables and solve problems with important distributions such as Bernoulli, binomial, geometric, and Poisson distributions;
• identify continuous random variables and solve problems with important distributions such as uniform, normal, and exponential distributions;
• define what expectation and variance mean and be able to compute them;
• calculate moments of random variables and derive the distributions of functions of random variables;
• compute the covariance and correlation between jointly distributed variables;
• identify random process and what wide sense stationary process mean;
• compute power spectral density through LTI system. 
課程要求
 Linear Algebra, Differential Equations, and Signals and Systems [may be taken concurrently]
ME 5057 is perhaps the most mathematically challenging course in the ME curriculum. We will use all you have learned in calculus and linear algebra to do something you have never seen before. Therefore, we require all students to be fluent in calculus and linear algebra. If you are uncertain whether you are ready to take ME 5057, please talk to Dr. Lin.
We will try to minimize the dependency of the course “Signals and Systems” in the first half of the semester. However, we expect you to be prepared for the Fourier Transforms when we start to discuss about moment generating functions (MGF). 
預期每週課後學習時數
  
Office Hours
 另約時間 備註： By email appointment with ME 5057 in the Subject line 
指定閱讀
 A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, Prentice Hall, 3rdEd, 2008.
While you are not required to purchase the textbook, you are encouraged get a copy. There are two reasons. First, lectures are intended to highlight the key concepts of the topics. We will not have time to go over all the details (e.g., derivation, proofs) in lectures. This is where the textbook will help you. Second, the textbook contains many interesting examples that can demonstrate the concepts. Reading them carefully. 
參考書目
 D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2nd Ed, 2008.
The book by Bertsekas and Tsitsiklis is an excellent text on probability. It contains many good examples, and problems with solutions. It also provides many pictorial illustrations. Sometimes these pictures can help you understand the material better. 
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 Homework 
0% 
 Homework will not be graded, but the some questions in the homework will be in the quiz. 
2. 
 Quiz 
20% 
 (4% each). There will be a 20-minute quiz in class. In each quiz, you will solve several questions chosen from homework. Quizzes are closed-book, closed-note. No electronics, including calculators, cell phones, and smart watches are allowed. Some formulas and tables may be provided. 
3. 
 Computer Assignment 
10% 
 (5% each). There will be two computer assignments in this course. You are required to use MATLAB or Python to solve the questions. The assignments should be done individually. 
4. 
 Mid-terms 
40% 
 (20% each). There are two mid-term exams in this course. Each mid-term is for 90 minutes. The mid terms are scheduled on – Mid-term 1: Oct 28 in class. – Mid-term 2: Dec 09 in class. Mid-terms are closed-book, closed-note. No electronics, including calculators, cell phones, and smart watches are allowed. Mid-terms will be used to access demonstration of the learning objectives and may include the combinations of true & false, multiple choices, and work-out problems. Some formulas and tables may be provided. 
5. 
 Fianl 
30% 
 The final is closed-book, closed- note. No electronics, including calculators, cell phones, and smart watches are allowed. The final is cumulative and may include the combinations of true & false, multiple choices, and work-out problems. Some formulas and tables may be provided. 
 
課程進度
週次
日期
單元主題
第1週
 9/23  Introduction, Set Theory, Probability Model, Conditional Probability, Bayes' Theorem 
第2週
 9/30  Total Probability, Independence, Discrete RV,
PMF, Expectation 
第3週
 10/07  Variance, Bernoulli, Binomial, Geometric RV, Poisson, Continuous RV, PDF, CDF 
第4週
 10/14  Expectation, Variance, Uniform, Exponential, Gaussian, Function of One Random Variable, 
第5週
 10/21  Function of One RVs, Multiple RVs,
Joint CDF, Joint PDF, IID, Joint Expectation 
第6週
 10/28  Midterm I,
Covariance, Correlation, Conditional RV 
第7週
 11/04  Conditional RV, Conditional PMF of Two RVs 
第8週
 11/11  Conditional Expectation Examples, Sum of Two RVs 
第9週
 11/18  Moment Generating Function, Characteristic Function, Joint Characteristic Function 
第10週
 11/25  Two Functions of Two RVs, MMSE Estimator, WLLN, CLT, Random Process 
第11週
 12/02  Mean Function, Autocorrelation Function, Stationary Process 
第12週
 12/09  Midterm II,
WSS, Power Spectral Density 
第13週
 12/16  Random Process through LTI System,
Cross Correlation through LTI System 
第14週
 12/23  Random Vectors, Joint Gaussian, MLE, MAP 
第15週
 12/30  Review 
第16週
 1/06  Final Exam