Everything we do, everything that happens around us, obeys the laws of probability. We can no more escape them than we can escape gravity... "Probability," a philosopher (Bishop Butler) once said, "is the very guide of life." We are all gamblers who go through life making countless bets on the outcome of countless actions.

Every field of science is concerned with estimating probability. A physicist calculates the probable path of a particle. A geneticist calculates the chances that a couple will have blue-eyed children. Insurance companies, businessmen, stockbrokers, sociologists, politicians, military experts - all have to be skilled in calculating the probability of the events with which they are concerned.

[Gardner, 1986]

Synopsis

Probability theory is the branch of mathematics that tells us how to estimate degrees of probability. If an event is certain to happen, it is given a probability of 1. If it is certain not to happen, it has a probability of 0.

This course introduces the principles of probability and random processes to undergraduate students in electronics and communication. The topics to be covered include random experiments, events, probability, discrete and continuous random variables, probability density function, cumulative distribution function, functions of random variables, expectations, law of large numbers, central limit theorem, introduction to random processes, Gaussian random process, autocorrelation and power spectral density.

Announcements

  • No class on Aug 30. Make-up class on Sep 3 (Monday) 10:40-12:00.
  • Slides for Announcements [Posted at 3:30PM on July 17]
  • No class on July 19 (TU Wai Kru Day)
  • Make up classes [Posted at 3:30PM on July 3]
    • July 6 (Friday) 9-10:20
    • July 9 (Monday) 10:40-12:00
  • A basic RSS feed is created to track and inform updates
  • This site can be accessed via prapun.com/ecs315
  • Welcome to ECS315! Feel free to look around this site.

General Information

Handouts and Course Material

  • Slides: Introduction to ECS315 [Posted @ 6:30 PM on June 26; Updated @ 3PM on July 5]
  • Part I: Classical Probability
  • Part II: Kolmogorov's Formal Probability Theory and Event-Based Probability Theory
  • Part III: Discrete Random Variables
  • Information regarding the midterm exam
    • 14 Aug 2012 TIME 13:30 - 16:30
    • ROOM BKD 2401
    • Closed book. Closed notes. No cheat/study sheet.
    • Basic calculators, e.g. FX-991MS, are permitted
    • 9 Pages + 1 Cover Page
    • 9 Problems + 1 Extra-Credit Problem
    • Cover all the materials that we discussed in class and practice in the HWs.
    • 2010 Midterm
      • Ignore Q3c, Q5-Q9. The topics havn't been discussed this year and hence won't be on the exam.
  • Part III (Con't)
    • Annotated version of Part III.1 [Posted @ 4PM on Aug 23; Updated @ 4 PM on Aug 28]
    • Part III.2 (Sections 8.3-8.4 and 9) [Posted @ 10PM on Aug 22]
      • Annotated version of Part III.2 [Posted @ 4PM on Aug 23; Updated @ 4PM on Sep 3, @ 3PM on Sep 4, @ 2PM on Sep 6, @11:30AM on Sep 12, and @7:30PM on Sep 13]
      • Quiz 4 Solution
      • Slides: Slides for Section 8 [Updated @ 9AM on Sep 4]
      • Slides: Slides for Section 9 [Posted @ 2PM on Sep 6]
    • Part III.3 (Sections 10.1-10.2) [Posted @ 10PM on Aug 22]
      • Annotated version [Posted @7:30PM on Sep 13; Updated @4PM on Sep 18 and @4PM on Sep 25]
    • Part III.4 (Sections 10.3 - 10.5) [Posted @ 10PM on Sep 16]
    • References:
      • A Pair of Random Variables: [Y&G] Sections 4.1 to 4.3 and Section 4.10
      • Extending the Definitions to Multiple RVs: [Y&G] Sections 5.1 to 5.4
      • Function of Discrete Random Variables: [Y&G] Section 4.6 (Theorem 4.9)
      • Expectation of function of discrete random variables: [Y&G] Sections 4.7 and 6.1
      • Linear Dependence: [Y&G] Section 4.7
  • Part IV
    • Part IV.1 (Sections 11.1-11.4) [Posted @ 10AM on Sep 25]
    • Part IV.2 (Sections 11.5-11.7) [Posted @ 2:30PM on Oct 3]
    • References
      • From Discrete to Continuous Random Variables: [Y&G] Sections 3.0 to 3.1
      • PDF and CDF: [Y&G] Sections 3.1 to 3.2
      • Expectation and Variance: [Y&G] Section 3.3
      • Families of Continuous Random Variables: [Y&G] Sections 3.4 to 3.5
      • Table 3.1 and Table 3.2 from [Y&G]
      • SISO: [Y&G] Section 3.7; [Z&T] Section 5.2.5
      • Pairs of Continuous Random Variables: [Y&G] Sections 4.1, 4.5, and 4.11
      • MISO: [Y&G] Section 6.2
  • Part V
  • Appendix
  • Information regarding the final exam
    • 13:30 - 16:30; 18 Oct 2012; BKD 2501-2
    • Closed book. Closed notes.
    • Basic calculators, e.g. FX-991MS, are permitted.
    • One A4 sheet allowed.
      • One side should be Table 3.1 and Table 3.2. (The sheet was distributed in class, but you can print your own sheet using the provided pdf file.)
      • Must be hand-written.
      • No small pieces of paper notes glued/attached on top of it.
      • Indicate your name and id on the upper right corner of the sheet.
      • Submit your formula sheet with your final exam. (You can get it back from me next semester.)
    • 11 Pages + 1 Cover Page
    • 9 Problems + 1 Extra-Credit Problem
    • Cover all the materials that we discussed in class and practice in the HWs.
    • Approximate score distribution based on sections taught in lecture:
      • 8:5%, 9:25%, 10:40%, 11:20%, 12to14:5%
    • More information may be posted here. [Updated @ 10PM on Oct 13]

Problem Set

  1. HW 1 (Due: July 20)
    • Solution [Posted @ 8:30AM on July 25]
    • Q7 was graded. See this file for some comments.
  2. HW 2 (Due: Aug 1)
  3. HW 3 (Due: Aug 10)
  4. Self-Evaluation (Due: Aug 24)
  5. HW4 (Due: Sep 6)
  6. HW5 (Due: Sep 13)
  7. HW6 (Due: Sep 25)
  8. HW7 (Due: Oct 4)
  9. HW8 (Due: Oct 11)
    Solve the following questions from [Yates & Goodman, 2005]
    Q3.1.3, Q3.2.1, Q3.2.3 (Change U,u to W,w), Q3.3.4, Q3.3.6, Q3.4.5
  10. HW9 (Free)
  11. Self-Evaluation (Due: Oct 18)

Calendar



Reading Assignment

Misc. Links