GTx: Probability and Statistics II: Random Variables – Great Expectations to Bell Curves

Upon completion of this course, learners will be able to:

• Identify discrete and continuous random variables
• Describe the properties of random variables, including the expected value, variance, and moment generating function.
• Understand functions of random variables, and how they can be used in computer simulation applications.
• Recognize joint (two-dimensional) random variables and how to extract marginal (onedimensional) and conditional information from them
• Implement the concepts of independence and correlation
• Work with and implement the R statistical package

“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)

*What if I don’t remember much basic probability?

Answer: You can take the companion course, “A Gentle Introduction to Probability”, which will get you up to speed lickety split!

*Will there be much programming?

Answer: A little, but you’ll be able to handle that in Excel or Matlab or whatever your favorite programming application is. We also go over a couple of R demos, but those will be self-contained.