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Probability and Statistics II: Random Variables – Great Expectations to Bell Curves
Course
en
English
24 h
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- Self-paced
- Free Access
- Fee-based Certificate
- 4 Sequences
- Intermediate Level
Course details
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: Univariate Random Variables
- Lesson 1: Introduction (FCPS §2.1)
- Lesson 2: Discrete Random Variables (FCPS §2.2)
- Lesson 3: Continuous Random Variables (FCPS §2.3)
- Lesson 4: Cumulative Distribution Functions (FCPS §2.4)
- Lesson 5: Great Expectations (FCPS §2.5.1)
- Lesson 6: LOTUS, Moments, and Varience (FCPS §2.5.2)
- Lesson 7 [OPTIONAL]: Approximations to E[h(X)] and Var(h(X)) (FCPS §2.5.3)
- Lesson 8: Moment Generating Functions (FCPS §2.6)
- Lesson 9: Some Probability Inequalities (FCPS §2.7)
- Lesson 10: Functions of a Random Variable (FCPS §2.8.1)
- Lesson 11: Inverse Transform Theorem (FCPS §2.8.2)
- Lesson 12 [OPTIONAL]: Honors Bonus Results (FCPS §2.8.3)
Module 2: Bivariate Random Variables
- Lesson 1: Introduction (FCPS §§3.1.1−3.1.3)
- Lesson 2: Marginal Distributions (FCPS §3.1.4)
- Lesson 3: Conditional Distributions (FCPS §3.2)
- Lesson 4: Independent Random Variables (FCPS §3.3.1)
- Lesson 5: Consequences of Independence (FCPS §3.3.2)
- Lesson 6: Random Samples (FCPS §3.3.3)
- Lesson 7: Conditional Expectation (FCPS §3.4.1)
- Lesson 8: Double Expectation (FCPS §3.4.2)
- Lesson 9 [OPTIONAL]: First-Step Analysis (FCPS §3.4.3)
- Lesson 10 [OPTIONAL]: Random Sums of Random Variables (FCPS §3.4.3)
- Lesson 11 [OPTIONAL]: Standard Conditioning Argument (FCPS §3.4.3)
- Lesson 12: Covariance and Correlation (FCPS §3.5.1)
- Lesson 13: Correlation and Causation (FCPS §3.5.2)
- Lesson 14: A Couple of Worked Correlation Examples (FCPS §3.5.3)
- Lesson 15: Some Useful Covariance / Correlation Theorems (FCPS §3.5.4)
- Lesson 16: Moment Generating Functions, Revisited (FCPS §3.6)
- Lesson 17 [OPTIONAL]: Honors Bivariate Functions of Random Variables (FCPS §3.7)
Prerequisite
Learners will be expected to come in knowing a bit of set theory and basic calculus, as well as the material from the first course in this series (A Gentle Introduction to Probability). The prerequisite material is all available for you to access; and in any event, we will make the current course as self-contained as possible. In addition, this course will involve a bit of computer programming, so it would be nice to have at least a little experience in something like Excel.
Instructors
David Goldsman
Professor of Industrial and Systems Engineering
The Georgia Institute of Technology
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