January 23, 2004
Probability Theory -- Events
We introduce the concepts of events and random variables in the context of rolling two dice. This experiment allows for a certain amount of complexity, but we can easily write down the entire sample space.
Bivariate Statistics
We conclude our discussion of descriptive statistics with a discussion of bivariate descriptive statistics. We supplement that with a preview of the probability theory for covariance and correlation.
To motivate student interest in these topics, we consider their application to portfolio analysis. If agents think of the tradeoff between expected return (expected value) and risk (variance), then understanding how to determine the expected return and risk for a portfolio aX+bY is fundamental. A portfolio manager might well seek out investment combinations with negative correlations to minimize portfolio risk.