課程資訊
課程名稱
 機率方法
Probabilistic Methods in Engineering 
開課學期
 112-1 
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
 星期四3,4,5(10:20~13:10) 
上課地點
 綜402 
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
  
預期每週課後學習時數
 3-4 
Office Hours
  
指定閱讀
  
參考書目
 A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, Prentice Hall, 3rd Ed, 2008. 
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 some questions with the homework assignments will be on the exam. 
2. 
 Computer Assignment 
20% 
 (10% 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. 
3. 
 Midterms 
50% 
 (25% 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: October 19 in class. – Mid-term 2: November 23 in class. Mid-terms are closed-book, closed-notes. No electronics, including calculators, cell phones, or 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 choice, and work-out problems. Some formulas and tables may be provided. 
4. 
 Final Exam 
30% 
 The date of the final exam will be on December 21. The final is closed-book, closed- notes. No electronics, including calculators, cell phones, or smart watches are allowed. The final is cumulative and may include the combinations of true & false, multiple choice, 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
 09/07  Introduction, Set Theory, Probability Model, Conditional Probability, Bayes' Theorem 
第2週
 09/14  Total Probability, Independence, Discrete RV, PMF, Expectation 
第3週
 09/21  Variance, Bernoulli, Binomial, Geometric RV, Poisson, Continuous RV, PDF, CDF 
第4週
 09/28  NO CLASS 
第5週
 10/05  Expectation, Variance, Uniform, Exponential, Gaussian, Function of One Random Variable 
第6週
 10/12  Function of One RVs, Multiple RVs, Joint CDF, Joint PDF, IID, Joint Expectation 
第7週
 10/19  Midterm I 
第8週
 10/26  Conditional RV, Conditional PMF of Two RVs Covariance, Correlation, Conditional RV 
第9週
 11/02  Conditional Expectation Examples, Sum of Two RVs 
第10週
 11/09  Moment Generating Function, Characteristic Function, Joint Characteristic Function 
第11週
 11/16  Two Functions of Two RVs, Random Vectors, Joint Gaussian, Estimation, MLE 
第12週
 11/23  Midterm II 
第13週
 11/30  MAP, MMSE, Limit Theorems, WLLN 
第14週
 12/07  WLLN, CLT, Random Process, Mean Function, WSS, Auto Correlation function, Stationary Process 
第15週
 12/14  Power Spectrum, Random Process through LTI System, Cross Correlation through LTI System 
第16週
 12/21  Final Exam