1. Prepare (due Mon 2/10)
   1. Content below
   2. Canvas quizzes
2. Class engagement – See on the class forum
3. Homework (due Sun 2/16, late due Thurs 2/20) [Link]
4. Worked Examples [Link]

Content (Slides in the Box folder)

5.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.)

5.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

Helpful YouTube videos to understand nuance with examples

• But what is the Central Limit Theorem? by 3Blue1Brown
• This is How Easy It Is to Lie With Statistics by Zach Star
  
• The medical test paradox, and redesigning Bayes’ rule by 3Blue1Brown
• How Long Can We Live? by MinuteEarth
• Understanding Cancer Survival Rates by vlogbrothers
• MIT OpenCourseWare The Chebyshev Inequality – If you’ve taken calculus, here is an explanation with that notation.
• MIT OpenCourseWare The Markov Inequality – If you’ve taken calculus, here is an explanation with that notation.

In the slides Box folder you will find additional resources on understanding Chebyshev and Markov

Online Textbook and Documentation

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:

• Python random – Base Python library
• Numpy random – Numpy random sampling library