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]


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.


  • Information regarding the final exam
    • 10 Oct 2013
    • 9:00 - 12:00
    • Building: IT & MT; Room: BKD 2601, 2605
    • 11 Pages: Cover page + 9 pages + 1 blank page
    • 9 Questions: 8 + 1 extra credit.
    • Closed book. Closed notes.
    • Basic calculators, e.g. FX-991MS, are permitted.
    • One A4 sheet allowed.
      • It should contain 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.)
      • Except the tables above, the rest of the content 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 next semester.)
    • Cover all the materials that we discussed in class and practice in the HWs.
      • Strong focus on the materials that haven’t been on the midterm.
      • 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.
      • Approximate Material Distribution (score-wise):
        • Sections 7-9: 25%
        • Section 10: 25%
        • Section 11.1-11.5: 30%
        • Section 11.6-11.7: 10%
        • Section 12-14: 10%
    • These notes are provided for your studying pleasure....
    • Tips:
      • Check your answers. To do this, think about alternative ways to find answers. For example, the expected value of Y = g(X) can be found directly from the pdf of X via the LOTUS formula. However, we can also find it from the pdf of Y as well.
      • Usually, there are many parts in a problem; some of these parts may also have subparts. If some quantity is defined in a part, then that quantity is used throughout the corresponding subparts. For example, if a random variable X is defined in part (c) of problem 3. Then, this definition of X is valid throughout parts c.i, c.ii, c.iii, ... Take alook at the first problem of the 2011 final exam, note how the definition of the joint pdf is used in part (a) to (l).
      • The answer(s) from earlier part(s) of a question may be useful for subsequent part(s) or question(s). You may refer to your own answer(s) from earlier part(s).
    • More information may be posted here.
  • Midterm scores are now available. Visit Dr.Prapun's office to take a look at your graded exam.
  • Information regarding the midterm exam
    • 1 Aug 2013 TIME 9:00-12:00
    • ROOM BKD 2601 & 2602
    • 11 Pages + 1 Cover Page.
      • Read the information on the cover page now so that you don't have to waste time reading it again in the exam room.
    • 7 Questions + 1 Extra Credits.
    • Closed book. Closed notes. No cheat/study sheet.
    • Basic calculators, e.g. FX-991MS, are permitted
    • Cover all the materials that we discussed in class and practice in the HWs.
  • A basic RSS feed is created to track and inform updates.
  • This site can be accessed via ecs315.prapun.com.
  • Welcome to ECS315! Feel free to look around this site.

General Information

Handouts and Course Material

Problem Set

  1. HW 1 (Due: June 28)
  2. HW2 (Due: July 5)
  3. HW3 (Due: July 12)
  4. HW4 (Due: July 19)
  5. HW5 (Due: July 26)
  6. HW6 (Not Due)
  7. Seff-Evaluation (Due: Aug 23)
  8. HW7 (Due: Aug 30)
    • Some tips from the tutorial session on Aug 23.
    • Solution[Posted @8PM on Sep 11]
  9. HW8 (Due: Sep 6)
    • Some tips from the tutorial session on Aug 30.
    • Solution [Posted @8PM on Sep 11]
  10. HW9 (Due: Sep 13; Updated @8:30 PM on Sep 11)
  11. HW10 (Due: Sep 20)
  12. HW11 (Due: Sep 27)
  13. HW12 (Due: Oct 4)
  14. HW13 (Not Due)
  15. Self-Evaluation (Due: Oct 10)


Reading Assignment

Misc. Links