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David Goldsman
This course provides an introduction to basic statistical concepts.
Read more
This course provides an introduction to basic statistical concepts.
Read more
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.
Register for this course and see more details by visiting:
OpenCourser.com/course/k6jzhz/probability
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:
- 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
“FCPS” refers to the free text, A First Course in Probability and Statistics: free access is provided via a PDF file or as a book
Module 1: Distributions• Lesson 1: Bernoulli and Binomial Distributions (FCPS §4.1.1)• Lesson 2: Hypergeometric Distribution (FCPS §4.1.2)• Lesson 3: Geometric and Negative Binomial Distributions (FCPS §4.1.3)• Lesson 4: Poisson Distribution (FCPS §4.1.4)• Lesson 5: Uniform, Exponential, and Friends (FCPS §4.2.1–4.2.2)• Lesson 6: Other Continuous Distributions (FCPS §4.2.3)• Lesson 7: Normal Distribution: Basics (FCPS §4.3.1)• Lesson 8: Standard Normal Distribution (FCPS §4.3.2)• Lesson 9: Sample Mean of Normals (FCPS §4.3.3)• Lesson 10: The Central Limit Theorem + OPTIONAL Proof (FCPS §4.3.4)• Lesson 11: Central Limit Theorem Examples (FCPS §4.3.5)• Lesson 12 [OPTIONAL]: Extensions – Multivariate Normal Distribution (FCPS §4.4.1)• Lesson 13 [OPTIONAL]: Extensions – Lognormal Distribution (FCPS §4.4.2)• Lesson 14: Computer Stuff, including OPTIONAL Box-Muller Proof (FCPS §4.5)
Module 2: Getting Started with Statistics• Lesson 1: Introduction to Descriptive Statistics (FCPS §5.1.1)• Lesson 2: Summarizing Data (FCPS §5.1.2)• Lesson 3: Candidate Distributions (FCPS §5.1.3)• Lesson 4: Introduction to Estimation (FCPS §5.2.1)• Lesson 5: Unbiased Estimation (FCPS §5.2.2)• Lesson 6: Mean Squared Error (FCPS §5.2.3)• Lesson 7: Maximum Likelihood Estimation (FCPS §5.2.4)• Lesson 8: Trickier MLE Examples (FCPS §5.2.4)• Lesson 9: Invariance Property of MLEs (FCPS §5.2.4)• Lesson 10: Method of Moments Estimation (FCPS §5.2.5)• Lesson 11: Sampling Distributions (FCPS §5.3)
Good to know
Good to know
Know what's good ,
what to watch for , 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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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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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.
Review High School Algebra
Show steps
Probability and statistics build upon concepts from algebra.
Browse courses on
Algebra
Show steps
Show steps
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
Show steps
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
Show steps
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
Show steps
This course covers topics already introduced to you. This will allow you to get a head start.
Browse courses on
Probability Theory
Show steps
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
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.
Data Analyst
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.
Data Scientist
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.
Risk Analyst
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.
Quantitative 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.
Operations Research Analyst
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.
Financial 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.
Actuary
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.
Market Research Analyst
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.
Epidemiologist
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.
Biostatistician
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.
Business Analyst
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.
Survey Statistician
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.
Statistician II
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.
Assistant Statistician
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.
For more career information including salaries, visit:
OpenCourser.com/course/k6jzhz/probability
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.
Save
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.
Provides a comprehensive introduction to statistical inference, covering both foundational concepts and modern techniques. It valuable resource for students and practitioners alike.
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.
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.
Save
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.
Save
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.
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.
Is tailored specifically for students and practitioners in engineering and science fields, providing a practical approach to probability and statistics.
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.
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.
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.
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.
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.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/k6jzhz/probability
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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
August 18, 2025
- January 1, 2026
May 12, 2025
- August 10, 2025
January 6, 2025
- May 9, 2025
August 19, 2024
- January 1, 2025
May 13, 2024
- August 11, 2024
January 8, 2024
- May 12, 2024
Language
English
Transcript
English
This course belongs to a
collection
called
Statistics, Confidence Intervals and Hypothesis Tests. It's comprised of two courses:
- Probability and Statistics III: A Gentle Introduction to Statistics (viewing)
- Probability and Statistics IV: Confidence Intervals and Hypothesis Tests
Good to know
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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