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This monograph uses the Julia language to guide the reader through an exploration of the fundamental concepts of probability and statistics, all with a view of mastering machine learning, data science, and artificial intelligence. The text does not require any prior statistical knowledge and only assumes a basic understanding of programming and mathematical notation. It is accessible to practitioners and researchers in data science, machine learning, bio-statistics, finance, or engineering who may wish to solidify their knowledge of probability and statistics. The book progresses through ten independent chapters starting with an introduction of Julia, and moving through basic probability, distributions, statistical inference, regression analysis, machine learning methods, and the use of Monte Carlo simulation for dynamic stochastic models. Ultimately this text introduces the Julia programming language as a computational tool, uniquely addressing end-users rather than developers. It makes heavy use of over 200 code examples to illustrate dozens of key statistical concepts. The Julia code, written in a simple format with parameters that can be easily modified, is also available for download from the book’s associated GitHub repository online.See what **co-creators of the Julia language** are saying about the book:**Professor Alan Edelman, MIT:**__With “Statistics with Julia”, Yoni and Hayden have written an easy to read, well organized, modern introduction to statistics. The code may be looked at, and understood on the static pages of a book, or even better, when running live on a computer. Everything you need is here in one nicely written self-contained reference.__**Dr. Viral Shah, CEO of Julia Computing:**__Yoni and Hayden provide a modern way to learn statistics with the Julia programming language. This book has been perfected through iteration over several semesters in the classroom. It prepares the reader with two complementary skills - statistical reasoning with hands on experience and working with large datasets through training in Julia.__ Preface Contents 1 Introducing Julia 1.1 Language Overview 1.2 Setup and Interface 1.3 Crash Course by Example 1.4 Plots, Images, and Graphics 1.5 Random Numbers and Monte Carlo Simulation 1.6 Integration with Other Languages 2 Basic Probability 2.1 Random Experiments 2.2 Working with Sets 2.3 Independence 2.4 Conditional Probability 2.5 Bayes' Rule 3 Probability Distributions 3.1 Random Variables 3.2 Moment-Based Descriptors 3.3 Functions Describing Distributions 3.4 Distributions and Related Packages 3.5 Families of Discrete Distributions 3.6 Families of Continuous Distributions 3.7 Joint Distributions and Covariance 4 Processing and Summarizing Data 4.1 Working with Data Frames 4.2 Summarizing Data 4.3 Plots for Single Samples and Time Series 4.4 Plots for Comparing Two or More Samples 4.5 Plots for Multivariate and High-Dimensional Data 4.6 Plots for the Board Room 4.7 Working with Files and Remote Servers 5 Statistical Inference Concepts 5.1 A Random Sample 5.2 Sampling from a Normal Population 5.3 The Central Limit Theorem 5.4 Point Estimation 5.5 Confidence Interval as a Concept 5.6 Hypothesis Tests Concepts 5.7 A Taste of Bayesian Statistics 6 Confidence Intervals 6.1 Single Sample Confidence Intervals for the Mean 6.2 Two Sample Confidence Intervals for the Difference in Means 6.3 Confidence Intervals for Proportions 6.4 Confidence Interval for the Variance of a Normal Population 6.5 Bootstrap Confidence Intervals 6.6 Prediction Intervals 6.7 Credible Intervals 7 Hypothesis Testing 7.1 Single Sample Hypothesis Tests for the Mean 7.2 Two Sample Hypothesis Tests for Comparing Means 7.3 Analysis of Variance (ANOVA) 7.4 Independence and Goodness of Fit 7.5 More on Power 8 Linear Regression and Extensions 8.1 Clouds of Points and Least Squares 8.2 Linear Regression with One Variable 8.3 Multiple Linear Regression 8.4 Model Adaptations 8.5 Model Selection 8.6 Logistic Regression and the Generalized Linear Model 8.7 A Taste of Time Series and Forecasting 9 Machine Learning Basics 9.1 Training, Testing, and Tricks of the Trade 9.2 Supervised Learning Methods 9.3 Bias, Variance, and Regularization 9.4 Unsupervised Learning Methods 9.5 Markov Decision Processes and Reinforcement Learning 9.6 Generative Adversarial Networks 10 Simulation of Dynamic Models 10.1 Deterministic Dynamical Systems 10.2 Markov Chains 10.3 Discrete Event Simulation 10.4 Models with Additive Noise 10.5 Network Reliability 10.6 Common Random Numbers and Multiple RNGs How-to in Julia A.1 Basics A.2 Text and I/O A.3 Data Structures A.4 Data Frames, Time-Series, and Dates A.5 Mathematics A.6 Randomness, Statistics, and Machine Learning A.7 Graphics Additional Julia Features Additional Packages Bibliography List of Julia Code Index "This monograph uses the Julia language to guide the reader through an exploration of the fundamental concepts of probability and statistics, all with a view of mastering machine learning, data science, and artificial intelligence. The text does not require any prior statistical knowledge and only assumes a basic understanding of programming and mathematical notation. It is accessible to practitioners and researchers in data science, machine learning, bio-statistics, finance, or engineering who may wish to solidify their knowledge of probability and statistics. The book progresses through ten independent chapters starting with an introduction of Julia, and moving through basic probability, distributions, statistical inference, regression analysis, machine learning methods, and the use of Monte Carlo simulation for dynamic stochastic models. Ultimately this text introduces the Julia programming language as a computational tool, uniquely addressing end-users rather than developers. It makes heavy use of over 200 code examples to illustrate dozens of key statistical concepts. The Julia code, written in a simple format with parameters that can be easily modified, is also available for download from the book's associated GitHub repository online. See what co-creators of the Julia language are saying about the book: Professor Alan Edelman, MIT: With "Statistics with Julia", Yoni and Hayden have written an easy to read, well organized, modern introduction to statistics. The code may be looked at, and understood on the static pages of a book, or even better, when running live on a computer. Everything you need is here in one nicely written self-contained reference. Dr. Viral Shah, CEO of Julia Computing: Yoni and Hayden provide a modern way to learn statistics with the Julia programming language. This book has been perfected through iteration over several semesters in the classroom. It prepares the reader with two complementary skills - statistical reasoning with hands on experience and working with large datasets through training in Julia." -- Publisher's description Introducing Julia -- Basic Probability -- Probability Distributions -- Processing and Summarizing Data -- Statistical Inference Concepts -- Confidence Intervals -- Hypothesis Testing -- Linear Regression and Extensions -- Machine Learning Basics -- Simulation of Dynamic Models -- Appendix A: How-to in Julia -- Appendix B: Additional Julia Features -- Appendix C: Additional Packages