Probability & Statistics

Probability theory and mathematical statistics study the regularities behind random phenomena: whether something will happen, how confident you can be that it will, and what conclusions a batch of observations actually supports. The subject has two halves. Probability theory supplies the language and the tools for describing a random world — sample spaces, random variables, distributions, numerical characteristics, and the large-sample theorems such as the law of large numbers and the central limit theorem. Mathematical statistics turns those tools around and points them at data: estimating unknown parameters from finite observations, placing intervals around the estimates, and deciding when the evidence contradicts a hypothesis. Readers should be comfortable with functions, limits, and series before starting.