STAT394A

Summer 2022, University of Washington

Course Description

This is the first quarter of a sequence in probability theory. This quarter, we will present the axioms of probability, that is, the tools to measure the uncertainty of some events. We will introduce the concepts of conditional and independent events. Then we will define what are random variables, how do we characterize discrete and continuous random variables by means of their probability mass or density functions. We will define what is the expectation and variance of a random variable, as well as how we compute these quantities using the probability mass or density functions. We will introduce classical distributions, such as the Bernoulli, binomial, geometric, Poisson, uniform, exponential, and Gaussian distributions. Finally, we will introduce the Law of Large Numbers and the Central Limit Theorem, which are the essential theorems that allow us to move from our theory to concrete estimations of some random variables.

Syllabus

By the end of MATH/STAT 394, students will be able to…

  1. Better understand different views of “randomness” in the context of probability and statistics
  2. Define and apply the following terms/concepts among others: probability, statistics, sample space, probability model, random variable, probability distribution, conditional probability, conditional independence
  3. Identify which probability rules to apply when, and correctly apply them
  4. Take a description of a sampling problem and formulate it in terms of a probability model
  5. Recognize some common probability distributions
  6. Determine when the binomial distribution can be well approximated by normal or Poisson
  7. Apply Bayes’ theorem
  8. Calculate expectation and variance from a pdf/pmf
  9. Compute a confidence interval for a sample proportion

This is an accelerated course, covering a quarter-length course in 4.5 weeks so that students can complete the two-quarter sequence over the summer.

Lecture slides

Before each class, I posted slides with blank space for the students to fill in as we worked through examples and took notes together. After each class, I posted my annotated slides.

Homework assignments

  • Homework 1 pdf
  • Homework 2 pdf
  • Homework 3 pdf
  • Homework 4 pdf

Acknowledgements

I developed these slides and homework assignments based on those from previous instructors Vincent Roulet and Aaron Osgood-Zimmerman.