Probability theory is a fundamental branch of mathematics that deals with the analysis of random phenomena. It is widely used in engineering to model and predict the behavior of complex systems. This course is designed to provide engineers with a solid understanding of the principles of probability theory and its applications in engineering.

Course Outline

  • Introduction to Probability:

    • Basic concepts of probability
    • Sample spaces and events
    • Conditional probability and independence

  • Discrete Random Variables:

    • Probability distributions
    • Expected value and variance
    • Common discrete distributions

  • Continuous Random Variables:

    • Continuous probability distributions
    • Expected value and variance
    • Common continuous distributions

  • Joint Distributions:

    • Joint probability distributions
    • Conditional probability distributions
    • Marginal probability distributions

  • Limit Theorems:

    • Law of large numbers
    • Central limit theorem

  • Applications in Engineering:

    • Reliability engineering
    • Queuing theory
    • Stochastic processes

Course Materials

  • Textbook: "Probability, Statistics, and Random Processes for Engineers" by A. Papoulis
  • Lecture Notes: Available on the course website

Prerequisites

  • Basic knowledge of calculus
  • Understanding of basic probability concepts

Course Resources

For further reading, you can explore the following resources:

Probability_Distribution