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

4 Weeks

$ 199

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Brief Introduction

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.

Description

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.

Knowledge

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