Chapter 2 is now ready for downloading—it can be found at this link.
This chapter is all about basic probability, with an emphasis on understanding and not on mechanics. Because of this, many details are eliminated which are usually found in standard books. If you already know combinatorial probability (taught in every introductory class), you will probably worry your favorite distribution is missing (“What, no Poisson? No negative binomial? No This One or That One?”). I leave these out for good reason.
In the whole book, I only teach two distributions, the binomial and the normal. I hammer home how these are used to quantify uncertainty in observable statements. Once people firmly understand these principles, they will be able to understand other distributions when they meet them.
Besides, the biggest problem I have found is that people, while they may be able to memorize half a dozen distributions or formulas, do not understand the true purpose of probability distributions. There is also no good reason to do calculations by hand now that computers are ubiquitous.
Comments are welcome. The homework section (like in every other chapter) is unfinished. I will be adding more homework as time goes on, especially after I discover what areas are still confusing to people.
Once again, the book chapter can be downloaded here.