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

Description

In this course, you will learn:

• Determine whether random variables are discrete or continuous.
• The expected value, variance, and moment generating function are all properties of random variables.
• Determine the functions of random variables and how to apply them in computer simulations.
• Recognize and extract marginal (one-dimensional) and conditional information from joint (two-dimensional) random variables.
• Remember the terms "independence" and "correlation."
• Work with the R statistical software and put it to use.

Syllabus:

1. Univariate Random Variables

• Introduction (FCPS §2.1)
• Discrete Random Variables (FCPS §2.2)
• Continuous Random Variables (FCPS §2.3)
• Cumulative Distribution Functions (FCPS §2.4)
• Great Expectations (FCPS §2.5.1)

2. Univariate Random Variables

• Moment Generating Functions (FCPS §2.6)
• Some Probability Inequalities (FCPS §2.7)
• Functions of a Random Variable (FCPS §2.8.1)
• Inverse Transform Theorem (FCPS §2.8.2)

3. Bivariate Random Variables

• Introduction (FCPS §§3.1.1−3.1.3)
• Marginal Distributions (FCPS §3.1.4)
• Conditional Distributions (FCPS §3.2)
• Independent Random Variables (FCPS §3.3.1)
• Consequences of Independence (FCPS §3.3.2)
• Random Samples (FCPS §3.3.3)
• Conditional Expectation (FCPS §3.4.1)
• Double Expectation (FCPS §3.4.2)

4. Bivariate Random Variables

• Random Sums of Random Variables (FCPS §3.4.3)
• Standard Conditioning Argument (FCPS §3.4.3)
• Covariance and Correlation (FCPS §3.5.1)
• Correlation and Causation (FCPS §3.5.2)
• A Couple of Worked Correlation Examples (FCPS §3.5.3)
• Some Useful Covariance / Correlation Theorems (FCPS §3.5.4)
• Moment Generating Functions, Revisited (FCPS §3.6)

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