What are the Chances? Probability and Uncertainty in Statistics
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Course Summary
Learn about the fundamentals of probability and statistics, including topics like probability theory, random variables, and hypothesis testing in this comprehensive course.Key Learning Points
- Understand the basics of probability theory and statistical inference
- Learn to apply probability models to real-world problems
- Explore the different types of probability distributions and hypothesis testing
- Gain the skills needed to analyze and interpret data using statistical methods
Related Topics for further study
Learning Outcomes
- Apply probability models to real-world problems
- Analyze and interpret data using statistical methods
- Communicate statistical findings effectively
Prerequisites or good to have knowledge before taking this course
- Basic knowledge of algebra and calculus
- Familiarity with programming concepts
Course Difficulty Level
IntermediateCourse Format
- Self-paced
- Online
- Video lectures
- Interactive quizzes
Similar Courses
- Introduction to Data Science
- Data Analysis with Python
- Statistics with R
Related Education Paths
Notable People in This Field
- Statistician and Founder of FiveThirtyEight
- Statistician and Data Visualization Expert
Related Books
Description
This course focuses on how analysts can measure and describe the confidence they have in their findings. The course begins with an overview of the key probability rules and concepts that govern the calculation of uncertainty measures. We’ll then apply these ideas to variables (which are the building blocks of statistics) and their associated probability distributions. The second half of the course will delve into the computation and interpretation of uncertainty. We’ll discuss how to conduct a hypothesis test using both test statistics and confidence intervals. Finally, we’ll consider the role of hypothesis testing in a regression context, including what we can and cannot learn from the statistical significance of a coefficient. By the end of the course, you should be able to discuss statistical findings in probabilistic terms and interpret the uncertainty of a particular estimate.
Outline
- Probability Theory
- Welcome Video
- Probability Definitions and Axioms
- Permutations and Combinations
- Conditional Probability and Independence
- Axiomatic Probability: Definition, Kolmogorov’s Three Axioms
- Monty Hall Simulation
- Combinations and Permutations
- Probability: Joint, Marginal and Conditional Probabilities
- Dependent Events and Independent Events
- Probability Definitions and Axioms Practice Problems
- Permutations and Combinations Practice Problems
- Conditional Probability Practice Problems
- Final Assessment on Probability Theory
- Random Variables and Distributions
- Random Variables and Probability Distributions
- The Normal Distribution
- Large Sample Theorems
- Random Variables
- Discrete Random Variables and Continuous Variables
- The Normal Distribution
- Central Limit Theorem: Definition and Examples in Easy Steps
- The Law of Large Numbers vs. The Central Limit Theorem
- Random Variables and Probability Distributions Practice Problems
- The Normal Distribution Practice Problems
- Large Sample Theorems Practice Problems
- Final Assessment on Random Variables and Distributions
- Confidence Intervals and Hypothesis Testing
- Bias, Consistency and the Standard Error
- Confidence Intervals
- Hypothesis Testing: Overview
- Hypothesis Testing: Implementation
- Bias vs. Consistency
- What are confidence intervals in statistics?
- What is hypothesis testing?
- Bias, Consistency and the Standard Error Practice Problems
- Confidence Intervals Practice Problems
- Hypothesis Testing Practice Problems
- Final Assessment on Confidence Intervals and Hypothesis Testing
- Quantifying Uncertainty in Regression Analysis and Polling
- Testing Regression Coefficients
- Pitfalls of Hypothesis Testing
- The Margin of Error in Polls
- Statistical Hypothesis Testing and Some Pitfalls
- Margin of Error: Definition, How to Calculate in Easy Steps
- Testing Regression Coefficients Practice Problems
- Pitfalls of Hypothesis Testing Practice Problems
- Margin of Error Practice Problems
Summary of User Reviews
This course on Chances, Probability, Uncertainty, and Statistics has received high praise from many users. The course covers a wide range of topics in an engaging and accessible way, and the instructor is highly knowledgeable and passionate about the subject matter. One key aspect that many users thought was good is the practical applications of the concepts covered in the course, which make it easy to understand and apply the knowledge to real-world scenarios.Pros from User Reviews
- Engaging and accessible course
- Highly knowledgeable and passionate instructor
- Practical applications of concepts covered
Cons from User Reviews
- Some users found the course material too basic
- Course pacing could be improved
- Some users felt that the course lacked depth in certain areas
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