After a brief introduction to the reasons for studying probability and statistics, the course treats the fundamentals of probability theory: sample spaces, events and their probabilities, conditional probability and independence, discrete and continuous random variables, simulation, expectation and variance, functions of random variables, joint distributions, and covariance and correlation. It finishes with discussions of the two most important theorems of the subject, the law of large numbers and the central limit theorem. This is the first course in a two semester sequence, the second course being devoted to statistics. |