Advanced Probability and Statistical Methods
Master advanced statistical concepts including joint distributions, hypothesis testing, and Markov chains with practical R implementation for data analysis.
Master advanced statistical concepts including joint distributions, hypothesis testing, and Markov chains with practical R implementation for data analysis.
This course cannot be purchased separately - to access the complete learning experience, graded assignments, and earn certificates, you'll need to enroll in the full Statistical Methods for Computer Science Specialization program. You can audit this specific course for free to explore the content, which includes access to course materials and lectures. This allows you to learn at your own pace without any financial commitment.
Instructors:
English
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What you'll learn
Analyze relationships between random variables through joint probability distributions and independence concepts
Calculate and interpret expected values, variances, and correlations for various probability distributions
Apply statistical limit theorems including the Central Limit Theorem, Markov inequality, and Chebyshev inequality
Conduct statistical hypothesis tests and T-tests with proper confidence intervals
Implement regression analysis techniques for data modeling and prediction
Construct and analyze Markov chains for systems with memoryless properties
Skills you'll gain
This course includes:
8.03 Hours PreRecorded video
22 assignments
Access on Mobile, Tablet, Desktop
FullTime access
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There are 6 modules in this course
This comprehensive course provides an in-depth exploration of advanced probability theory and statistical methods essential for data-driven decision making in computer science. Students begin with joint distributions of multiple random variables, both discrete and continuous, exploring independence concepts and conditional probabilities. The curriculum progresses through expectation theory, covering expected values, variance, covariance, and correlation, with emphasis on applying the linearity of expectation to solve complex problems. Important statistical theorems and inequalities including the Central Limit Theorem, Markov inequality, and Chebyshev inequality are examined in detail. Later modules focus on practical statistical testing methodologies, including hypothesis testing, T-tests, and regression analysis. The course concludes with an extensive study of Markov chains and Poisson processes, introducing concepts of memoryless properties, limiting probabilities, and entropy calculations. Throughout all modules, theoretical concepts are reinforced with practical R programming implementations and real-world problem-solving exercises.
Course Introduction
Module 1 · 11 Minutes to complete
Joint Distributed Random Variables
Module 2 · 13 Hours to complete
Expectation
Module 3 · 12 Hours to complete
Inequalities and Central Limit Theorem
Module 4 · 8 Hours to complete
Statistical Testing
Module 5 · 6 Hours to complete
Markov Chain
Module 6 · 6 Hours to complete
Fee Structure
Instructors
Pioneering Social Network Analysis and AI at Johns Hopkins University
Dr. Ian McCulloh is an esteemed associate professor at Johns Hopkins University, holding joint appointments in the Bloomberg School of Public Health and the Whiting School of Engineering. His research focuses on social neuroscience, social network analysis, and the application of artificial intelligence to enhance understanding of online influence and strategic communication. With over 100 peer-reviewed publications and several influential books, including Social Network Analysis with Applications and ISIS in Iraq: Understanding the Social and Psychological Foundations of Terror, Dr. McCulloh has established himself as a leading voice in his field. He also founded the Brain Rise Foundation, a nonprofit dedicated to advancing neuroscience research for substance abuse recovery. Prior to his academic career, he had a distinguished military service, retiring as a Lieutenant Colonel after 20 years, during which he led innovative projects in data-driven social science research for countering extremism. Dr. McCulloh's multifaceted expertise and commitment to applying science for societal benefit make him a valuable asset to both academia and public health initiatives.
Instructor at Johns Hopkins University
Tony Johnson, affiliated with Johns Hopkins University, is an expert in teaching English courses, focusing on advanced probability and statistical methods. His teaching style emphasizes practical applications of statistical concepts to real-world problems
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