Statistics Foundations: Understanding Probability and Distributions
We live in a world of big data, and someone needs to make sense of all this data. In this course, you will learn to efficiently analyze data, formulate hypotheses, and generally reason about what the ocean of data out there is telling you.
What you'll learn
We live in a world of big data: huge amounts of data generated by social networks, governments, consumers and markets. Someone needs to make sense of all this data. In this course, Statistics Foundations: Understanding Probability and Distributions, you will learn the fundamental topics essential for understanding probability and statistics. First, you will have an introduction to set theory, a non-rigorous introduction to probability, an overview of key terms and concepts of statistical research. Then, you will discover different statistical distributions, discrete and continuous random variables, probability density functions, and moment generating functions. Finally, you will use key distribution measures such as mean and variance, and explore topics of covariance and correlation. By the end of this course, you’ll be able to look at data and reason about it in terms of its descriptive statistics and possible distributions.
Table of contents
- Course Introduction 4m
- Module Overview 1m
- Introducing Sets 3m
- Set Membership, Null Set, Subsets 5m
- Set Operations: Union, Intersect, Difference 3m
- Cardinality and Set Complement 2m
- Some Set Laws 2m
- Experiments and Events 2m
- Sample Spaces and Points 1m
- Set Operations on Events 2m
- Independence of Events 1m
- Demo: Set Operations 5m
- Introduction to Probability 3m
- Rules of Probability 1m
- Probability Examples 2m
- Demo: Basic Probability 5m
- Discrete and Continuous Probability 3m
- Counting Sample Points 3m
- Multiplication Rule 1m
- Permutations 5m
- Permutation Examples 3m
- Demo: Birthday Problem 6m
- Combinatorial Methods 4m
- Binomial Coefficients 4m
- Multinomial Coefficients 4m
- Probability of a Union of Events 4m
- Summary 1m
- Overview 1m
- Random Variables 5m
- Discrete Random Variables 5m
- Discrete Uniform Distribution 2m
- Binomial Distribution 3m
- Geometric Distribution 4m
- Hypergeometric Distribution 3m
- Continuous Distributions 9m
- Continuous Uniform Distribution 2m
- Normal Distribution 6m
- Gamma Distribution 3m
- Beta Distribution 4m
- Summary 1m
- Overview 1m
- Expectation 6m
- Mean 4m
- Expectation for a Continuous Distribution 4m
- Functions of a Random Variable 3m
- Law of the Unconscious Statistician 2m
- Properties of Distributions 2m
- Variance 6m
- Moments and the Moment Generating Function 7m
- Means and Variance of Some Distributions 4m
- Demo: Mean and Variance 3m
- Joint Distributions 2m
- Probability Mass Function 3m
- Functions of 2 or More Random Variables 3m
- Marginal PDFs 2m
- Covariance and Correlation 7m
- Demo: Covariance and Correlation 3m
- Summary 1m
About the author
Dmitri Nesteruk is a quantitative analyst, developer, speaker, and podcaster. His interests lie in software development and integration practices in the areas of computation, quantitative finance, and algorithmic trading. He is an instructor of an entry-level course in Quantitative Finance. His technological interests include C#, F#, and C++ programming as well high-performance computing using technologies such as CUDA. He has been a C# MVP since 2009.