These class notes are the currently used textbook for “Probabilistic Systems
Analysis,” an introductory probability course at the Massachusetts Institute of
Technology. The text of the notes is quite polished and complete, but the problems
are less so.
The course is attended by a large number of undergraduate and graduate
students with diverse backgrounds. Acccordingly, we have tried to strike a balance
between simplicity in exposition and sophistication in analytical reasoning.
Some of the more mathematically rigorous analysis has been just sketched or
intuitively explained in the text, so that complex proofs do not stand in the way
of an otherwise simple exposition. At the same time, some of this analysis and
the necessary mathematical results are developed (at the level of advanced calculus)
in theoretical problems, which are included at the end of the corresponding
chapter. The theoretical problems (marked by *) constitute an important component
of the text, and ensure that the mathematically oriented reader will find
here a smooth development without major gaps.
We give solutions to all the problems, aiming to enhance the utility of
the notes for self-study. We have additional problems, suitable for homework
assignment (with solutions), which we make available to instructors.