ENGR 3341: Probability and Statistics

Spring 2021

Instructor Aria Nosratinia,
ECSN 4.504, Tel: 972-883-2894
Time Tuesdays and Thursdays 2:30pm-3:45pm
Place Virtual/Remote
Textbook Pishro-Nik, Introduction to Probability, Statistics, and Random Processes (required)
Please also see the textbook web page
Yates and Goodman, Probability and Stochastic Processes, 2nd Edition John Wiley. (optional)
The textbook is available from the UTD Bookstore, Off Campus Books, as well as Amazon Barnes and Noble, and other sources.
Grading Class participation (5%), Quizzes (5%), 3 Midterms (50%), Final Exam (40%)
Exams Midterms: TBA, Final Exam: TBA
Exam locations: Virtual/Remote
Prerequisite Calculus
Office Hours Tuesdays and Thursdays 1:30pm-2:15pm
TA Information: TBA

Probability and statistics are used everywhere around us. You only have to look at the polls in this election year to see an interesting application of probability. Banks use probability to determine how many tellers to have available to maximize efficiency. Wall street traders use sophisticated stochastic optimization tools. Airlines use probability to find out how to arrange their routes to maximize profits.

Wireless communications (cell phones and WiFi) would be impossible without probability tools and techniques. Probability is also used to characterize reading and writing of bits on magnetic media. Without it your laptop computer, portable music player, and game stations such as Xbox, Wii, Playstation, would not work.

So why do we use probability to begin with? Because there are times when it is fundamentally impossible to determine the outcome of an experiment with complete certainty, or make a measurement with great precision. At times it may be possible, but not economical. Either way, we use probability to glean knowledge and make decisions in the presence of uncertainty.

This course gives an introduction to the fundamentals of probability and statistics with an eye to engineering applications.

Contents:

  • Probability Basics
    • Set Theory
    • Probability Axioms
    • Conditional Probability and independence
    • Combinatorics
  • Discrete Random Variables
    • Probability distributions (cdf)
    • Probability mass functions (densities, pdf)
    • Examples of r.v.
    • Averages and Moments
    • Function of a r.v.
  • Continuous Random Variables
    • cdf and pdf of continuous r.v.
    • averages and moments
    • Gaussian, Laplacian, and other useful r.v.
    • Functions of a continuous r.v.
  • Multiple Random Variables
    • Joint probability distributions
    • Joint densities
    • Marginal densities
    • Conditional distributions/densities
    • Gaussian densities
  • Sums and Limit Theorems
    • Expectation of sums
    • Moment generating function
    • Central limit theorem
  • Elements of Statistical Analysis
    • Sample mean and variance
    • Confidence intervals