Module 03: Probability

Module
  1. Prepare (due M 1/24)
    1. Content below
    2. Sakai quizzes
  2. Peer Instructions – See on the class forum
  3. Homework (due Su 1/30)
  4. Worked Examples

Content (Slides in the Box folder)

3.A – Foundations of Probability (52 min.)

  1. Outcomes, Events, Probabilities (15 min.)
  2. Joint and Conditional Probability (11 min.)
  3. Marginalization and Bayes’ Theorem (15 min.)
  4. Random Variables and Expectations (11 min.)

3.B – Distributions of Random Variables (46 min.)

  1. Distributions, Means, Variance (19 min.)
  2. Monte Carlo Simulation (15 min.)
  3. Central Limit Theorem (12 min.)
    1. Slide 26 in the video has a typo that is fixed in the pdf version of the slides on Box. In the video, it says the probability is <= 0.95, but it should say < 0.05.

Optional Supplements

You can access an excellent free online textbook on OpenIntro Statistics here, co-authored by Duke faculty. You can pay a suggested but adjustable price for a tablet-friendly pdf, but you can also just get the regular pdf for free. For this module, the following optional readings may be particularly helpful supplements:

  • Chapter 3: Probability. This provides more information on many of the topics from the above videos in Foundations of Probability.
  • Chapter 4: Distributions of random variables. This provides much more information about particular classic distributions than is provided in 2B.B.1.
  • Chapter 5.1: Point estimates and sampling variability. This provides more information on some of the topics from 2B.B.2-3.

In addition, you can find documentation for the two pseudorandom number generating / sampling libraries in python that we mentioned here: