Introduction to probability [electronic resource] / Joseph K Blitzstein; Jessica Hwang.

Probability and counting Conditional probability Random variables and their distributions Expectation Continuous random variables Moments Joint distributions Transformations Conditional expectation Inequalities and limit theorems Markov chains Markov chain Monte Carlo Poisson processes.

"Undergraduate probability book that assumes one-semester of calculus. One key is the emphasis on "stories" for the probability distributions (which I mean in both an intuitive and technical sense): there are a dozen or so key distributions (Normal, Binomial, Poisson, etc.) that are incredibly widely-used in statistics, but a lot of books just write down formulas for them without explaining clearly why these particular distributions are so important, or how they are all connected. Each of these distributions has a "story" (a natural application where it arises), and thinking about stories makes the distributions easier to remember, understand, and work with"-- Provided by publisher.