Offering: Step By Step Probability

Titles: Step By Step Probability I, Probability: Audible Lecture Series

By Dr. Michael Kouritzin

Preface

In recent years, many high schools have started to cover basic probability and statistics to help students cope with their early university probability courses. While today's students have a greater scope of mathematical knowledge and sophistication, they still struggle immensely in their first couple of courses in university probability. For example, the combined dropout/failure rate is often in the range of 15 to 20 per cent for each probability course taught to computer scientists, engineers etc. These probability courses are considered difficult due because of students' typically weak math backgrounds.

The goal for this text is to prepare students for interdisciplinary work or study in, for example, mathematical finance, computational science, engineering or applied mathematics by exposing statistical problems requiring computer solutions to those most capable of solving them. We have chosen the material presented here with these reasons in mind.

We feel it is important to delve reasonably deep into the most important topics with the aim of provoking thought. We have striven to enliven the material by taking an application-motivated, mathematically solid approach. In particular, experience working with probabilistic and statistical methods is more important than the actual topics covered. Therefore, we have chosen the motivational applications from those listed as favourites from previous students. We certainly hope that you will enjoy and benefit from the material as much as we believe you will.

This text focuses primarily on discrete probability, random vectors and stochastic processes, along with their applications to gambling, data processing and mathematical finance. Naturally, the amount of effort required for a course depends upon your background and relative abilities. Like all things in life, nothing comes for free; your earnest effort is required for success.

Here we describe the layout and purpose of the subsections listed below that the reader will encounter in this text.

Review

Sections start with a “Review” of the prerequisite topics needed to successfully understand the particular section.

Synopsis

Sections have a“Synopsis” summarizing the materials that a reader can expect to learn from that particular section.

Warm-up Questions

Some sections have “Warm-up Questions” that the reader should be able to answer without reading any further. We suggest that you try to figure out the answers to these problems before reading a particular section.

Questions to Ponder

The main subject matter may start with the “Questions to Ponder”. Keep these in mind when going through the rest of the section’s subject matter. By the end of the section, you should be able to answer these questions.

Cool Fact

Some sections have this added, fun discussion to broaden your horizon of knowledge on certain topics; these are not meant as materials on which you should be tested.

Questions

Sections have a “Questions” subsection. These are the workbook questions that a reader should practice to master the skills learnt from a particular section.