Introduction to Probability

Format:

Book

Author/Creator:

Baxter, John R., author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Statistics--Textbooks.

Statistics.

Physical Description:

1 online resource

Place of Publication:

Minneapolis, Minnesota John R. Baxter 2023.

Language Note:

In English.

Summary:

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.

Contents:

Contents

Preface

Probability and Events

Assumptions for probability, and their consequences

Models with continuous sample spaces

Conditional probability

Independence and its consequences

Tricky little problems

Independent sequences

Counting

Random variables

Expected values, finite range case

More properties of expected value

Independent random variables, first applications

Waiting times

Random variables with countable range

Exponential waiting times

Moments and inequalities

Poisson random variables

Normal random variables and the Central Limit Theorem

Appendices

Bibliography

Index

Notes:

Description based on online resource