Foundations of Probability and Random Variables
Master fundamental probability concepts, combinatorial analysis, and random variables with practical R programming applications for data science.
Master fundamental probability concepts, combinatorial analysis, and random variables with practical R programming applications for data science.
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
Master combinatorial techniques including permutations, combinations, and multinomial coefficients
Apply probability axioms to evaluate probabilities in various scenarios using Venn diagrams
Utilize Bayes' formula and conditional probability to solve complex real-world problems
Analyze discrete random variables using probability mass functions and expected values
Work with continuous random variables and understand their probability density functions
Implement probability concepts in R programming for data analysis and simulations
Skills you'll gain
This course includes:
10.37 Hours PreRecorded video
21 assignments
Access on Mobile, Tablet, Desktop
FullTime access
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There are 6 modules in this course
This comprehensive course provides a solid foundation in probability theory and random variables, essential for computational methods in computer science and data science. Beginning with combinatorial analysis, students learn to solve counting problems using permutations, combinations, and multinomial coefficients. The curriculum progresses through probability axioms, Venn diagrams, and sample space calculations before exploring conditional probability, independence concepts, and Bayes' formula for analyzing event relationships. Later modules cover both discrete and continuous random variables, teaching students to work with probability mass functions, probability density functions (PDFs), cumulative distribution functions (CDFs), and expected values. Special attention is given to important distributions including Bernoulli, uniform, and normal distributions. Throughout the course, theoretical concepts are complemented with practical R programming exercises that help students apply probability concepts to real-world problems through simulations and data analysis, preparing them for advanced studies in machine learning, AI, and algorithm design.
Course Introduction
Module 1 · 14 Minutes to complete
Combinatorial Analysis
Module 2 · 5 Hours to complete
Probability
Module 3 · 8 Hours to complete
Conditional Probability and Independence
Module 4 · 9 Hours to complete
Discrete Random Variables
Module 5 · 13 Hours to complete
Continuous Random Variables
Module 6 · 10 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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