機率

臺北科技大學 114-2 學期課程，課號 355221。

課程大綱

The course of probability considers events that may or may not occur. It provides mathematical and logical models to describe random phenomena occurred in natural science, engineering, and social behaviors. This course is an important branch of applied mathematics. The basic theory and numerous applications will be covered.

課程進度

Week 1. Introduction to Probability; Counting Principle Week 2. Permutations and Combinations Week 3. Sample Spaces, Event and Axioms of Probability Week 4. Some Propositions; Equally Likely Fundamental Events Week 5. Conditional Probability; Bayes Formula Week 6. Independent Events; Sequential Events Week 7. Midterm 1; Random Variables Week 8. Discrete random Variable, CDF, PMF Week 9. Expectation, Variance, and Well Known Discrete Random Variables. Week 10. Continuous Random Variable and PDF Week 11. Well Known Continuous random Variables Week 12. Function of a Random Variable; Midterm 2 Week 13. Two and Multi Dimensional Random Variables Week 14. (Expectations of) Sums of Random Variables Week 15. Correlation and Covariance; Conditional Expectation Week 16. Inequality, the Law of Large Numbers and Limit Theorems Week 17. Selected Topics (Poisson Process, Markov Chain etc) Week 18. Final Exam

評量方式

1. Homeworks + Class participation 20% 2. Two Mid Term Exams. 50% 3. Final Exam. 30%

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Please refer to (https://istudy.ntut.edu.tw/learn/index.php) for course website, announcement and updated information。 Textbook: Ghahramani, “Fundamentals of Probability with Stochastic Processes,” 3rd ed., Pearson, 2005 (or PNIE edition, 2014) , or 4th ed., CRC Press, 2019. Reference Books: 1. S. Ross, “A First Course in Probability”, 7th ed., Pearson Prentice Hall, 2006. 2. Leon-Garcia, “Probability and Random Processes for Electrical Engineering,” 3rd ed., Pearson, 2009. 3. Yates and Goodman, “Probability and Stochastic Processes,” 3rd ed., John Wiley & Sons, 2015. 4. Papoulis and Pillai, “Probability, Random Variables, and Stochastic Processes,” 4th ed., Mc-Graw-Hill, 2002. 5. Walpole, Myers, Myers and Ye, “Probability and Statistics for Engineers and Scientists,” 9th ed., Pearson, 2014.