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This course discusses properties and applications of random variables. For instance, how many customers are likely to arrive in the next hour? What’s the probability that a lightbulb will last more than a year?
When you’re done with this course, 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.
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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.
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.
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
Module 2: Bivariate Random Variables
*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.
