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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.
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

# Randomness, Probability, and Random Variables

This is a dense section, with many theoretical concepts to learn. Although it is heavy, you will finish this section with a very good grasp of some of the most basic and foundational concepts in probability theory. We will also introduce very useful methods you can use to perform simulations using NumPy so that you get to play around with some code. By using simulations, we hope to show you how the theoretical concepts translate into actual numbers and problems that can be solved with these tools. Finally, we will define random variables and probability distribution, two of the most important concepts to know about when using statistics to solve problems in the real world.

## Randomness and Probability

We all have an intuitive idea of the concept of randomness and use the term in everyday life. Randomness means that certain events happen unpredictably or without a pattern.