The goal of this book is to give a brief yet comprehensive overview of the most commonly used probability distributions. For each distribution, we will include frequently used formulas for the probability mass/density function, expectation, and variance. More importantly, examples will be used to illustrate the use cases for each distribution.
Probability is a way of expressing how likely an event is to happen. An event with a probability of 0 corresponds to no chance of it happening, whereas a probability of 1 corresponds to an absolute certainty that it will happen.
Our world is filled with uncertainty What is the likelihood that I will need my umbrella tomorrow? What will the inflation rate be next year? What are the survival chances of a breast cancer patient? Probability helps us address these types of questions, and in general, it helps us to make informed decisions despite the uncertainty.
This book serves as a guide for computing probabilities under different probability distributions. Prerequisites include an understanding of basic probability, although a quick review will be presented in this book. A good textbook on basic probability is the third book listed in the References section. For the continuous probability distribution section of the book, knowledge of basic calculus, specifically knowledge of solving integrals, would be helpful.