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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.
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.
