This qualifies as a "first course" because it assumes no prior knowledge of probability. The units are numbered in the same order as they occur in the text, though they can obviously be used in any order.
An outline is included, indicating which modules contain the material and for those who desire to use the text's arrangement.
Ordinary calculus and the fundamentals of matrix algebra serve as the necessary mathematical requirements. We employ a few common series and integrals, and we evaluate double integrals as iterated integrals. The examples provide clear guidance on how to handle the iterated integrals used in the theory of expectation and conditional expectation for readers who are able to assess simple integrals.
The work describes and uses user-defined MATLAB procedures and functions (which we refer to as m-programs or simply programs), to solve many significant problems in basic probability, in addition to providing an introduction to the fundamental characteristics of basic probability in terms of a precise mathematical model. Because of this, it ought to be useful both as a standalone explanation and as an addition to any number of current textbooks.
The majority of the programs created here were originally created in earlier versions of MATLAB, however many have undergone small revisions to become fully compatible with MATLAB 7. Alternative implementations are available in the Statistics Toolbox in a few instances, however here they are implemented directly from the fundamental MATLAB program so that students only require that program (and the symbolic mathematics toolbox if they desire its aid in evaluating integrals).