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 electrical engineering. 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.

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General Information

Handouts and Course Material

  • Lecture notes are posted in Google Classroom
  • Part I: Introduction, Set Theory, Classical Probability theory, and Combinatorics
  • Part II: Kolmogorov's Formal Probability Theory and Event-Based Probability Theory
    • Chapter 5: Probability Foundations 
    • Chapter 6: Event-based Independence and Conditional Probability
  • Part III: Discrete Random Variables
    • Chapter 7: Random Variables [Posted @ 11AM on Oct 12]
    • Chapter 8: Discrete Random Variables [Posted @ 11AM on Oct 12]
      • Sections 8.1-8.2: PMF and CDF
      • Section 8.3-8.4: Families of Discrete Random Variables
    • Chapter 9: Expectation and Variance [Posted @ 2PM on Nov 3]
      • References: [Y&G] Chapter 2
  • Part IV: Continuous Random Variables
    • Chapter 10: Continuous Random Variables [Posted @ 2PM on Nov 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
  • Part V: Advanced Topics
    • Chapter 11: Multiple Random Variables
      • 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
    • Chapter 12: Limiting Theorems (LLN and CLT)
    • Chapter 13: Three Types of Random Variables
  • Appendix

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