This course discusses properties and applications of random variables. When you’re done, you’ll have enough firepower to undertake a wide variety of modeling and analysis problems; and you’ll be well-prepared for the upcoming Statistics courses.
We’ll begin by introducing the concepts of discrete and continuous random variables. For instance, how many customers are likely to arrive in the next hour (discrete)? What’s the probability that a lightbulb will last more than a year (continuous)?
We’ll learn about various properties of random variables such as the expected value, variance, and moment generating function. This will lead us to a discussion of functions of random variables. Such functions have many uses, including some wonderful applications in computer simulations.
If you enjoy random variables, then you’ll really love joint (two-dimensional) random variables. We’ll provide methodology to extract marginal (one-dimensional) and conditional information from these big boys. This work will enable us to
study the important concepts of independence and correlation.
Along the way, we’ll start working with the R statistical package to do some of our calculations and analysis.
“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)