Regression Notes - 1
This is the first notebook covering regression topics. It starts with basic estimation and diagnostics. This example uses a dataset I’m familiar with throu...
Lesson 1-1-2: Event Operations and Properties
This lesson explores event operations, specifically unions, intersections, and complementation, as well as the properties of these operations with detailed visualizations. I realize that despite my best efforts, some of the illustrations may not perfectly communicate the property in question, so it is important to try to understand the notation. If you’re on mobile, you can view the lesson here: Presentation 1-1-2 Event Operations and Properties
2020
Lesson 1-3-1: Conditional Probability
Now things are getting fun: We’re moving on to section 3, on conditional probability and independence! If you’re on mobile, you can view the lesson here: Pr...
Lesson R-1-2-6: Counting
This is the coding supplement to theory lesson 1-2-6. If you’re on mobile, view this lesson here: Lesson R-1-2-6: Counting. You can also download the code ...
Lesson 1-2-7: Finishing Up
Short final lesson on calculating probabilities by counting. If you’re on mobile, you can view the lesson here: Presentation 1-2-7: Finishing Up
Lesson 1-2-6: Learning to Count, Part 2
And now for the thrilling conclusion to our two-part lesson on counting! If you’re on mobile, you can view the lesson here: Presentation 1-2-6 Learning to Co...
Lesson 1-2-5: Learning to Count, Part 1
Think you know how to count? Well, think again! It’s time we covered the Fundamental Theorem of Counting! This two-part lesson will be followed up by a cod...
Lesson 1-2-4: Bonferroni’s Inequality (and some other stuff)
We’re pretty close to finishing the material from subsection 1.2.2: The Calculus of Probabilities. Enjoy this short lesson on Bonferroni’s Inequality. Next...
Lesson R-0-1: Prologue: Obtaining R
Pretty soon we’re gonna need to write some code. Luckily, I’m here to teach you how to do it! We’re gonna start by installing R and RStudio. Then, we’ll g...
Lesson 1-2-3: Axioms and Consequences
Now it’s getting serious. We’ve established the axioms of probability, but there is so much more to be done with them! Some of it, sadly, gets a little inv...
Lesson 1-2-2: The Axioms, Explained
Now we’re getting to the good stuff! We’re not only taking a deeper dive into the axioms of probability, we’re also proving that a (relatively) simple funct...
Lesson 1-2-1: Of Axioms and Algebras
We’re ready to start working toward an axiomatic definition of probability. First, however, we take a rather painful detour through the realm of Borel field...
Lesson 1-1-3: Set Theory Conclusion
This lesson rounds out our primer on set theory by introducing operators that allow us to take the union or intersection of many (or even infinitely many) se...
Lesson 1-1-2: Event Operations and Properties
This lesson explores event operations, specifically unions, intersections, and complementation, as well as the properties of these operations with detailed v...
Lesson 1-1-1: The Sample Space and Events
This lesson begins our journey with the introduction of the sample space, and the events therein. If you’re on mobile, you can view the lesson here: Present...