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Probability and Statistics III

A Gentle Introduction to Statistics

David Goldsman

This course provides an introduction to basic statistical concepts.

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This course provides an introduction to basic statistical concepts.

We begin by walking through a library of probability distributions, where we motivate their uses and go over their fundamental properties. These distributions include such important folks as the Bernoulli, binomial, geometric, Poisson, uniform, exponential, and normal distributions, just to name a few. Particular attention is paid to the normal distribution, because it leads to the Central Limit Theorem (the most-important mathematical result in the universe, actually), which enables us to make probability calculations for arbitrary averages and sums of random variables.

We then discuss elementary descriptive statistics and estimation methods, including unbiased estimation, maximum likelihood estimation, and the method of moments – you gotta love your MoM! Finally, we describe the t, X2, and F sampling distributions, which will prove to be useful in upcoming statistical applications.

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What's inside

Learning objectives

  • Review a library of discrete and continuous probability distributions
  • Recognize the normal distribution and the central limit theorem, and how they are applied in practice
  • Recognize elementary methods of descriptive statistics
  • Describe methods that can be used to estimate the unknown parameters of a distribution
  • Identify statistical sampling distributions
  • Upon completion of this course, learners will be able to:

Syllabus

Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Covers common probability distributions used in statistical analysis
Teaches the Central Limit Theorem and other concepts central to statistics
Explores descriptive statistics and estimation methods
Provides clear explanations of key statistical concepts and theory
Introduces sampling distributions, which are essential for statistical inferences

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Reviews summary

Gentle foundation in core statistics

According to learners, this course offers an incredibly clear and gentle introduction to foundational statistics, making complex concepts accessible. Many highlight the excellent instructor's ability to simplify topics like the Central Limit Theorem and Maximum Likelihood Estimation. Students praise the well-structured modules and the benefit of a free accompanying textbook, which aids in building a strong theoretical foundation. While lauded as a perfect starting point for beginners, some reviewers noted it might be too basic for those with prior experience and could benefit from more hands-on application and coding exercises to bridge theory with practical skills.
Ideal for beginners, but may be too basic for some learners.
"While 'gentle' it still requires dedication... The pace was mostly good, but some parts felt a bit rushed."
"For a 'Probability and Statistics III', I found this course surprisingly basic in many areas. If you already have some background, much of this will be review."
"I did feel that sometimes the 'gentle' introduction meant less depth than I eventually desired, but for what it sets out to do, it succeeds admirably."
Features organized modules and a valuable free textbook.
"The use of the free textbook was a huge bonus and I found the optional proofs very insightful."
"The syllabus is well-structured."
"The provided textbook is a valuable asset. The progression from basic distributions to CLT and estimation methods is logical and well-paced."
Builds a robust understanding of core statistical principles.
"Highly recommended for a solid foundation!"
"It built a strong foundation for me to move onto more advanced topics. Truly a 'gentle' yet comprehensive overview."
"This course is a cornerstone for anyone starting in data science or research."
Simplifies complex statistical concepts, ideal for beginners.
"As someone coming back to statistics... The instructor's explanations are incredibly clear, breaking down complex concepts like the Central Limit Theorem into understandable pieces."
"This course excels in making advanced topics like Maximum Likelihood Estimation accessible. The instructor's passion shines through..."
"Clear, concise, and incredibly well-taught. The Central Limit Theorem explanation was the best I've encountered. The instructor's ability to simplify without sacrificing accuracy is truly remarkable."
Focuses on theory, less on hands-on exercises or coding.
"Overall, a great course, but I felt a need for more hands-on practice."
"I sometimes wished for more interactive elements or coding exercises to solidify understanding. I needed to supplement with external resources for practical application."
"The theoretical explanations are thorough, but the course lacks practical exercises or assignments that truly apply the concepts using software."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Probability and Statistics III: A Gentle Introduction to Statistics with these activities:
Review High School Algebra
Probability and statistics build upon concepts from algebra.
Browse courses on Algebra
Show steps
  • Review your notes or find online resources to refresh your memory on the basics of algebra.
  • Practice solving algebra problems to regain your proficiency.
Review "Mathematical Statistics with Applications
Review a reference text on probability and statistics to refresh your memory and ensure a strong foundation prior to beginning this course.
View Mathematical Statistics with Applications on Amazon
Show steps
  • Read through the introduction of the book.
  • Summarize the contents of chapter 1.
  • Solve the exercises at the end of chapter 2.
Review Probability and Statistics Concepts
This course covers topics already introduced to you. This will allow you to get a head start.
Browse courses on Probability Theory
Show steps
  • Go over your notes from previous probability and statistics courses.
  • Read introductory materials on the topics covered in this course.
  • Solve practice problems to test your understanding.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Follow Online Tutorials on Statistical Software
Enhance your proficiency in statistical software by following guided tutorials that provide step-by-step instructions on how to use its features and functions.
Browse courses on Statistical Software
Show steps
  • Identify a reputable online learning platform.
  • Choose a tutorial that aligns with your learning goals.
  • Follow the instructions in the tutorial.
  • Practice using the software on your own.
Practice Probability and Statistics Problems
Sharpen your problem-solving skills by working through a collection of practice problems covering key concepts in probability and statistics.
Browse courses on Probability Distributions
Show steps
  • Identify the type of problem you are trying to solve.
  • Apply the appropriate statistical principles.
  • Calculate your answer.
  • Check your answer for accuracy.
Attend a Statistical Society Meeting
Connect with other statistics enthusiasts, learn about the latest research, and expand your professional network by attending a local or virtual meeting of the Statistical Society.
Browse courses on Networking
Show steps
  • Find a Statistical Society meeting near you.
  • Attend the meeting and introduce yourself.
  • Listen to the presentations and ask questions.
  • Network with other attendees.
Create a Statistical Infographic
Develop a visually appealing infographic that summarizes and makes sense of a complex statistical concept or real-world dataset.
Browse courses on Data Visualization
Show steps
  • Choose a topic that interests you.
  • Gather data from reliable sources.
  • Analyze the data using statistical methods.
  • Design an infographic using a tool like Canva or Piktochart.
  • Share your infographic with classmates or on social media.
Volunteer for a Data-Driven Organization
Apply your statistical knowledge and skills to make a meaningful impact by volunteering for an organization that uses data to drive decision-making and improve society.
Browse courses on Data Analytics
Show steps
  • Identify organizations that align with your interests.
  • Contact the organization and inquire about volunteer opportunities.
  • Attend training and orientation sessions.
  • Work on data-related projects under the guidance of experienced professionals.
  • Share your insights and contribute to the organization's mission.

Career center

Learners who complete Probability and Statistics III: A Gentle Introduction to Statistics will develop knowledge and skills that may be useful to these careers:
Statistician
Statisticians use statistical methods to collect, analyze, interpret, and present data. They work in a variety of industries, including healthcare, finance, and marketing. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics. The course covers the basics of sampling and experimental design, as well as how to analyze data.
See salaries and explore the career path for Statistician
Data Analyst
Data analysts collect and analyze data to help businesses make informed decisions. They use statistical methods to analyze data and identify trends. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Data Analyst
Data Scientist
Data scientists use statistical methods to analyze data and build predictive models. They work in a variety of industries, including technology, healthcare, and finance. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Data Scientist
Operations Research Analyst
Operations research analysts use statistical methods to improve the efficiency of business processes. They work in a variety of industries, including manufacturing, healthcare, and logistics. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Operations Research Analyst
Quantitative Analyst
Quantitative analysts use statistical methods to analyze financial data and make investment recommendations. They work in a variety of industries, including investment banking, asset management, and hedge funds. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Quantitative Analyst
Financial Analyst
Financial analysts use statistical methods to analyze financial data and make investment recommendations. They work in a variety of industries, including investment banking, asset management, and insurance. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Financial Analyst
Actuary
Actuaries use statistical methods to assess risk and uncertainty. They work in a variety of industries, including insurance, pensions, and healthcare. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Actuary
Risk Analyst
Risk analysts use statistical methods to assess risk and uncertainty. They work in a variety of industries, including insurance, banking, and healthcare. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Risk Analyst
Biostatistician
Biostatisticians use statistical methods to design and analyze clinical trials and other health-related studies. They work in a variety of settings, including universities, hospitals, and pharmaceutical companies. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Biostatistician
Market Research Analyst
Market research analysts use statistical methods to collect and analyze data about consumer behavior. They work in a variety of industries, including marketing, advertising, and product development. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Market Research Analyst
Epidemiologist
Epidemiologists use statistical methods to study the distribution and causes of disease. They work in a variety of settings, including public health agencies, hospitals, and universities. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Epidemiologist
Business Analyst
Business analysts use statistical methods to analyze data and make recommendations to improve business operations. They work in a variety of industries, including consulting, technology, and healthcare. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Business Analyst
Survey Statistician
Survey statisticians use statistical methods to design and analyze surveys. They work in a variety of settings, including government agencies, businesses, and non-profit organizations. This course can help you develop the skills you need to succeed in this role by providing you with a strong foundation in probability and statistics.
See salaries and explore the career path for Survey Statistician
Statistician II
Work independently to perform statistical analyses and prepare reports. Conduct research to identify optimal statistical methods for data analysis. Develop and implement quality control procedures to ensure the accuracy and reliability of statistical data. May supervise the work of other statisticians.
See salaries and explore the career path for Statistician II
Assistant Statistician
Assist senior statisticians with the collection, analysis, and interpretation of data. Prepare statistical reports and presentations. May provide technical support to other researchers.
See salaries and explore the career path for Assistant Statistician

Reading list

We've selected 13 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Probability and Statistics III: A Gentle Introduction to Statistics.
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All of Statistics
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Takes a unique approach to statistical inference, focusing on the fundamental concepts and principles that underlie all statistical methods. It thought-provoking read for students and practitioners who want to deepen their understanding of statistics.
All of Statistics: A Concise Course in Statistical...
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All of Nonparametric Statistics (Springer Texts in...
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All of statistics : A concise course in statistic...
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Statistical Inference
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Provides a comprehensive introduction to statistical inference, covering both foundational concepts and modern techniques. It valuable resource for students and practitioners alike.
Statistical Inference
Hardcover
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Statistical Inference
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Times Higher Education Abroad excellent selection...
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Bayesian Data Analysis, Third Edition
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Provides a comprehensive introduction to Bayesian data analysis, covering both theoretical concepts and practical applications. It valuable resource for students and practitioners who want to learn about Bayesian methods.
Bayesian Data Analysis (Chapman & Hall/CRC Texts in...
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The Elements of Statistical Learning
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Focuses on modern statistical learning methods, such as regression, classification, and clustering. It valuable resource for students and practitioners who want to learn about the latest advances in statistical modeling.
The Elements of Statistical Learning: Data Mining,...
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The Elements of Statistical Learning: Data Mining,...
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The Elements of Statistical Learning: Data Mining,...
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Deep Learning
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Provides a comprehensive overview of deep learning, covering both theoretical concepts and practical applications. It valuable resource for students and practitioners who want to learn about deep learning and its applications.
Deep Learning
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Deep Learning (Adaptive Computation and Machine...
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Deep Learning (Adaptive Computation and Machine...
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Data Mining
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Provides a comprehensive overview of data mining techniques, including both supervised and unsupervised learning methods. It valuable resource for students and practitioners who want to learn about data mining and its applications.
Data Mining: Practical Machine Learning Tools and...
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DATA MINING, 4TH EDITION
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Data Mining: Practical Machine Learning Tools and...
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Reinforcement Learning, second edition
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Provides a comprehensive introduction to reinforcement learning, covering both theoretical concepts and practical applications. It valuable resource for students and practitioners who want to learn about reinforcement learning and its applications.
Reinforcement Learning, second edition: An...
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Reinforcement Learning, second edition: An...
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Probability and Statistics for Engineers and...
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Is tailored specifically for students and practitioners in engineering and science fields, providing a practical approach to probability and statistics.
Probability & Statistics for Engineers & Scientists
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Probability and Statistics for Engineers and...
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Probability & Statistics for Engineers & Scientists
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Probability & Statistics for Engineers & Scientists...
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Probability and Statistics for Engineers and...
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Probability & Statistics for Engineers & Scientists...
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Mathematical Statistics with Applications
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This textbook provides a solid foundation in mathematical statistics, with a focus on applications in various fields. It useful reference for students and practitioners who need a deeper understanding of statistical theory.
Mathematical Statistics with Applications
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Mathematical Statistics with Applications
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Mathematical Statistics with Applications
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WebAssign Access Card for Mathematical Statistics...
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Mathematical Statistics with Applications
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Natural Language Processing with Python
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Provides a comprehensive introduction to natural language processing, covering both theoretical concepts and practical applications. It valuable resource for students and practitioners who want to learn about natural language processing and its applications.
Natural Language Processing with Python: Analyzing...
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Natural Language Processing with Python: Analyzing...
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Hands-On Machine Learning with Scikit-Learn, Keras,...
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Provides a practical guide to machine learning using popular Python libraries, such as Scikit-Learn, Keras, and TensorFlow. It valuable resource for students and practitioners who want to learn about machine learning and its applications.
Hands-On Machine Learning with Scikit-Learn, Keras,...
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Hands-On Machine Learning with Scikit-Learn, Keras,...
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Hands-On Machine Learning with Scikit-Learn, Keras,...
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Introduction to Probability and Mathematical...
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Offers a clear and concise introduction to probability and mathematical statistics, making it a suitable choice for students and practitioners with limited background in these areas.
Introduction to Probability and Mathematical...
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Introduction to Probability and Mathematical...
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Advanced High School Statistics
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This open-source textbook comprehensive resource for introductory statistics, covering both theoretical foundations and practical applications. It valuable supplement to the course, especially for students who prefer a more self-paced learning approach.
Advanced High School Statistics
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Advanced High School Statistics
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Course image
Effort
6 to 10 hours per week for 4 weeks
Level
Intermediate
Via
edX
Institution
The Georgia Institute of Technology
Instructor
David Goldsman
Sessions
August 17, 2026 - January 1, 2027 May 11, 2026 - August 9, 2026 January 5, 2026 - May 10, 2026
Language
English
Transcript
English
This course belongs to a collection called Statistics, Confidence Intervals and Hypothesis Tests. It's comprised of two courses:
  1. Probability and Statistics III: A Gentle Introduction to Statistics (viewing)
  2. Probability and Statistics IV: Confidence Intervals and Hypothesis Tests
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Covers common probability distributions used in statistical analysis
Teaches the Central Limit Theorem and other concepts central to statistics
Explores descriptive statistics and estimation methods
Provides clear explanations of key statistical concepts and theory
Introduces sampling distributions, which are essential for statistical inferences
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