ABSTRACT
Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 Cumulative Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5 Some Useful Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.6 Change of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.7 Derivation of the Normal Distribution Function . . . . . . . . . . . . . . . . 76 3.8 An Applied Sabbatical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.9 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.10 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.11 Numerical Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Much of the development of probability in Chapter 2 involved probabilities in the abstract. We briefly considered the distribution of rainfall, but we were largely interested in flipping coins or rolling dice. These examples are typically referred to as aleatoric – involving games of chance. In this chapter we develop somewhat more complex versions of probability which form the basis for most econometric applications. We will start by developing the uniform distribution that defines a frequently used random variable. Given this basic concept, we then develop several probability relationships. We then discuss more general specifications of random variables and their distributions.
