Introduction to Probability Theory

Probability theory underpins machine learning, furnishing tools to handle uncertainty and variability in data. As you embark on this journey, grasping the fundamentals of probability will be pivotal for your exploration of advanced statistical models and algorithms.

In this chapter, you will delve into the basic principles of probability, commencing with the definitions of probability and the axioms that form its foundation. You'll learn how to calculate probabilities in various contexts, utilizing both discrete and continuous models. Fundamental concepts such as random variables, probability distributions, and expected values will be introduced, paving the way for more intricate applications in subsequent chapters.

We'll explore the properties of common probability distributions, including the binomial, Poisson, and normal distributions. Understanding these distributions will be essential, as they frequently arise in machine learning tasks. You will also gain insights into the law of large numbers and the central limit theorem, two critical theorems that justify the use of probability in statistical inference and machine learning.

By the end of this chapter, you will have a solid comprehension of how probability theory provides a framework for reasoning about uncertainty, laying the groundwork for more sophisticated probabilistic models that you will encounter throughout this course.