1 / 12

Introduction to Probabilities in Electrical Engineering: A Comprehensive Overview

Explore the fundamentals and applications of probability theory in various fields, from signal processing to finance and physics. Delve into the history, concepts, and practical implications of probability, including statistical mechanics, quantum mechanics, and biomedicine. Understand key topics such as law of large numbers, central limit theorem, and Gaussian distribution. The syllabus covers essential chapters, exams, assignments, and resources for a thorough understanding of probabilities. Join the course to discover the intriguing world of probabilities in diverse disciplines.

buffy-strong
Télécharger la présentation

Introduction to Probabilities in Electrical Engineering: A Comprehensive Overview

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Probabilities Fall 2010 Dept. Electrical Engineering National Tsing Hua University 劉奕汶

  2. What is probability? • Literally, how probable an event is to occur. • We live in a random world • Relative-frequency interpretation • 機率／概率／或然率 • This interpretation is problematic • Involved law of large number • Not all experiments could be repeated • Not all repeating processes have convergent frequency • Axiomatic approach

  3. A bit of History • 3500 B.C., Egyptians used bones to gamble • Since then, dice, playing cards, mahjong, etc. • 15-16th centuries: Italy (Galilei et al.) • 17-18th centuries: Western-central Europe • Pascal, Fermat, Laplace, Poisson, Gauss • Huygens (1629-1695) On Calculations in Games of Chance • 19-20th : Russia • 1900: Hilbert’s 23 problems • 1933: Kolmogorov: probability theory axiomatized

  4. Probability in EE/CS • Signal processing • “Signal” = Random Process • Random because of noise and uncertainty • Machine learning • Natural language processing • Pattern recognition • Communication • Source coding • Channel coding • Modulation and estimation

  5. Probability in Finance/Economics • Investment / Gambling • Portfolio theory • Advertisement / Pricing

  6. Probability in Physics (i) • Statistical mechanics • Equilibrium • Entropy and 2nd law of thermodynamics • Definition of temperature

  7. Probability in Physics (ii) • Quantum mechanics • Schrödinger’s wave function • “Measurement makes reality” • The paradox of Schrödinger’s cat • Einstein’s famous comment

  8. Probability in Biomedicine • Genomics • Proteomics • Neuroscience • Ecology • Epidemiology

  9. Probability and Statistics • Law of Large Number • Central Limit Theorem • Why Gaussian distribution is “Normal” • Counter-example: stock market

  10. Syllabus • Textbook: S. Ghahramani, Fundamentals of Probability: with stochastic processes, 3rd Edition • Chapters 1-3: probability space • Chapters 4-5: discrete random variables • Chapter 6: Continuous random variables • Midterm exam (35%) • Chapters 7: continuous random variables II • Chapters 8: bivariate distributions • Chapter 10-11: advanced topics (Correlations, LLN, CLT, etc) • * Measure theory and axioms of probability • Final exam (35%) • A4 double-side cheat sheet permitted for both exams • 6 homework assignments (30%) • Office hours: Monday 5-6 pm, Rm 704B • Website: http://www.ee.nthu.edu.tw/ywliu/ee3060/

  11. Statistics of last semester’s grades (N = 37) • 期中考:M=51.4,SD=7.9 • 期末考:M=49.3,SD=10.8 • 總成績:M = 78,SD=11 • 36 passed, 1 failed. • 4 scored 90 or above (A+)

More Related