Essentials of Mathematical Probability and Statistics

This text is intended for a one-semester course in probability and statistics that presumes calculus knowledge up to integration techniques. It is perhaps helpful if a student has already been exposed to sequences and series but much of what is needed is reviewed in the text.

An interactive version of this text is available at

http://math.mc.edu/travis/mathbook/Probability/Essentials_Probability_And_Statistics.html² http://math.mc.edu/travis/mathbook/Probability/Essentials_Probability_And_Statistics.html

and an pdf version with active links is available at

http://math.mc.edu/travis/mathbook/Probability/Essentials_Probability_And_Statistics.pdf³ http://math.mc.edu/travis/mathbook/Probability/Essentials_Probability_And_Statistics.pdf .

A collection of WeBWorK online homework problems are available to correlate with the material in this text. Copies of these sets of problems are available by contacting the author. These exercises are considered an integral part when using this text although a static version of these is included in the appendix.

To successfully utilize this text, a student should review the requisite material and perhaps review the proofs and derivations if appropriate. While moving through the text, the student should review each of the examples and then attempt each of the interactive WeBWorK exercises. Whenever an interactive cell comes up, the student should play around with the cell and perhaps change the input data as appropriate to experiment. When a section is completed, a student should work the WeBWorK exercises (not part of this text) or some other exercises provided by the instructor and attempt the exercises provided in this text...many of which are famous examples or exercises that might have special significance. Some are (of course) just easy and most of the textbook exercises have solutions provided.

WeBWorK (webwork.maa.org⁴) is an open-source online homework system for math and science courses. WeBWorK is supported by the MAA and the NSF and comes with a Open Problem Library (OPL) of over 35,000 homework problems. Problems in the OPL target most lower division undergraduate math courses and some advanced courses. Supported courses include college algebra, discrete mathematics, probability and statistics, single and multivariable calculus, differential equations, linear algebra and complex analysis.

Sage (sagemath.org⁵) is a free, open-source, software system for advanced mathematics, which is ideal for assisting with a study of abstract algebra. Sage can be used either on your own computer, a local server, or on SageMathCloud (https://cloud.sagemath.com⁶).

R (https://www.r-project.org/⁷) is a programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing. The R language is widely used among statisticians and data miners for developing statistical software and data analysis. In this text, the sage cell is used also for interactive computations related to R.