機率

臺北科技大學 114-2 學期課程，課號 355279。

課程大綱

本課程介紹機率學的原理與應用。機率學為數學的一門學科，探討不確定事件或行為的數學表示及計算方式，廣泛應用於自然科學、工程及社會科學中。本課程之授課範圍，包含：1.組合分析、2.機率公設、3.條件機率與獨立事件、4.離散隨機變數、5.連續隨機變數、6.二維與多維隨機變數、7.期望值性質、8.極限定理。

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 Terms 25%*2=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 請於本課程北科i學園PLUS上，查詢本課程課程網頁、公告事項與即時訊息。 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.