Chapter 7

Probability Distributions and Random Variables


Bullet Understanding the concept of the random variable

Bullet Describing the behavior of a random variable with a probability distribution

Bullet Summarizing the properties of a random variable with moments

This chapter introduces two new concepts that are used to determine the probability that a random event takes place — random variables and probability distributions. These concepts are closely related to the notion of the random experiment (defined in Chapter 6). A random experiment is a process in which events unfold in an unpredictable way. A random variable is used to assign numerical values to all the possible outcomes of a random experiment. A probability distribution assigns probabilities to these numerical values.

In this chapter, I also define summary measures of a probability distribution, known as moments, such as expected value and variance. Random variables and probability distributions are used by economists, financial analysts, researchers, and others to model the behavior of economic and financial variables, such as interest rates, inflation rates, corporate earnings, and so on.

Defining the Role of the Random ...

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