| Major Topic | Subtopics |
| Introduction to Probability Theory |
Experiments, outcomes, and sample spaces |
| The coin toss experiment |
| Bernoulli trials |
| The Binomial experiment |
| R functions dbinom, pbinom, qbinom, and rbinom |
| Independence |
Tree diagrams |
| Independent events |
| Reliability and redundancy |
| Conditional Probability |
Definition of conditional probability |
| The Law of Total Probability |
| Baye's theorem |
| Applications of Baye's theorem |
| Frequentist and Bayesian Statistics |
The law of large numbers |
The central limit theorem |
| The classical or frequentist approach |
| The Bayesian approach |
| Markov chain monte carlo methods |
| Applications of Markov chain monte carlo methods |
| Bootstrap methods |
| Discrete probability distributions and their applications |
The geometric distribution |
| The negative binomial distribution |
| The Poisson distribution |
| The hypergeometric distribution |
| Continuous probability distributions and their applications |
The beta distribution |
| The gamma distribution |
| The normal distribution |
| The chi-square distribution |
| The t distribution |
| The F distribution |