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 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

  • All of your HWs are graded and put in the HW box. Please come and pick them up at your earliest convenience.
  • Scores for HW6 to HW10
  • Information about the Final Exam
    • 13 Oct 2010
    • 09:00 - 12:00
    • BKD 3215
    • 8 Questions: 31 pt + 15 pt + 22 pt + 27 pt + 3 pt + 1 pt + 1 pt + 1 bonus pt.
    • 12 Pages: 10 pages + 1 cover sheet + 1 blank sheet
      • Here is the first page of the exam.
    • Closed book / Closed notes
    • You will need a basic calculator e.g. FX-991MS.
    • It can cover all the materials that we discussed in class and practice in the HWs.
      • In particular, I expect that you know a little bit about LLN and CLT in 4a because we have talk about them a little bit in class.
      • In general, the topics that we spent a lot of time in class have high probability of showing up on the exam.
      • I could ask something that I have never defined in class but, in such a case, I will give you the exact definition on the exam itself.
    • One A4 sheet allowed.
      • 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.)
    • More information may be posted.
  • Scores for Quiz 5 and Quiz 6
  • Scores for Quiz 4
  • Scores for Quiz 3
  • Midterm:
    • 9 Questions
    • 10 pages + 1 cover sheet + 1 formula sheet
    • Closed book / Closed notes
    • You will need a basic calculator e.g. FX-991MS.
    • Here is the formula sheet created by you during the last lecture before the midterm.
    • Here is the first page of the exam.
    • The exam covers every topics that we have studied.
    • Scores
    • Solution (draft)
  • Scores for HW1-4 + Quiz 1-2. (The leftmost column contains the last three digits of your student IDs.)
  • There will be NO class on Wednesday, July 21. The makeup class will be the first period (9-10:20AM) on Friday (July 23). [Posted @ 1PM on July 19]
  • We will have the midterm on the ORIGINAL announced date. (6 Aug 2010 TIME 09:00 - 12:00 BUILDING IT & MT ROOM BKD 2605). Sorry for the confusion and for giving you some hope that the date might change. [Posted @ 1PM on July 19]
  • A basic RSS feed is created to track and inform updates [Posted @ 5PM on Jun 25]
  • This site can be access via prapun.com/ecs315 [Posted @ 5PM on Jun 25]
  • Welcome to ECS315! Feel free to look around this site. [Posted @ 5PM on Apr 1]

General Information

Handouts and Course Material

Problem Set

  1. HW 1 (Due: June 29)
    • Note: The correct version of the HW has just been uploaded @ 9PM on Thursday. A couple of questions are different.
    • Solution for HW1
  2. HW2 (Due: July 9 @10:39 AM in class)
    • Note: The version with updated due date of the HW is posted on July 4 @ 3:30 PM
    • Solution for HW2
      • Correction: The last conditional probability on page 2-7 is P(H|U).
  3. HW3 (Due: July 15)
  4. HW4 (Due: July 22)
    • Q4: Change lambda to alpha. (Usually, Poisson r.v. uses lambda as its parameter. In class, I use alpha. There are reasons for not using lambda which we shall revisit later on in the lecture.)
    • Q6: The mode may not be unique. If there are multiple x which attains the maximum pmf value, find all of them.
    • Solution for HW4 (draft)
    • Scores for HW1-4 + Quiz 1-2. (The leftmost column contains the last three digits of your student IDs.)
  5. HW5 with Solution (Not due) (Updated on Aug 3 @ 2:30 PM)
  6. HW6 (Due: Aug 27) [Fixed on August 24 @ 9PM]
  7. HW7 (Due: Sep 9)
  8. HW8 (Due: Sep 17) [Fixed on Sep 15 @ 2PM]
  9. HW9 (Due: Sep 27)
  10. HW10 (Official Due Date: Oct 1; Extended Due Date: Oct 6)

Calendar



Reading Assignment

  1. Probability Puzzles [Gardner, 1986] is available on the SIIT Lecture Note System
  2. Compound Chance Experiment and Bernoulli Trials

Course Outline

  1. Introduction, Classical probability, Mathematical background

  2. Counting Methods (Combinatorics)

  3. Probability Foundation

  4. Random variable (real-valued)

  5. Real-valued functions of a random variable

  6. Expectation, moment, variance, standard deviation, central moment

  7. Independence

  8. MIDTERM: 6 Aug 2010 TIME 09:00 - 12:00

  9. Function of random variables

  10. Random vectors

  11. Real-valued jointly Gaussian random vectors

  12. Summation of i.i.d. random variable and laws of large numbers

  13. Transform method: Characteristic function

  14. Central limit theorem

  15. Random processes, Cross-correlation and Power spectral density

  16. FINAL: 13 Oct 2010 TIME 09:00 - 12:00

Misc. Links