Assuming one semester of calculus, this textbook introduces probability to undergraduate students who want to learn statistics. It clearly explains the importance of widely used distributions in statistics, such as normal, binomial, and Poisson, and explores how they are all connected. The book makes the distributions easier to remember, understand, and work with by illustrating natural applications where they arise, including applications of MCMC. R is used to perform statistical calculations.

Table of Contents

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. Appendices. Bibliography.