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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Table of Contents (14 chapters)
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Introduction

In previous chapters, we have described and explored data using descriptive statistics and visual techniques. We have also looked at probability, randomness, and using simulations of random variables to solve problems. The idea of distributions was also examined, which plays a much bigger role later in this chapter.

When looking at applying statistical ideas, there are some important questions to answer concerning methodology. Some examples of these questions could include "how large should I make my sample?" or "how confident can we be in the results?". For this chapter, we will look at how we can apply two of the most important theorems in statistics, starting with their practical implications before moving onto solving common problems using the more useful techniques that are derived from these important ideas.

In this chapter, we will explain what the law of large numbers is and clarify how sample size affects the sample mean. The central...