Basic Statistical Concepts
One chapter cannot possibly review what one learned in one or two pre-requisite courses in statistics. This is an econometrics book, and it is imperative that the student have taken at least one solid course in statistics. The concepts of a random variable, whether discrete or continuous, and the associated probability function or probability density function (p. d.f.) are assumed known. Similarly, the reader should know the following statistical terms: Cumulative distribution function, marginal, conditional and joint p. d.f.’s. The reader should be comfortable with computing mathematical expectations, and familiar with the concepts of independence, Bayes Theorem and several continuous and discrete probability distributions. These distributions include: the Bernoulli, Binomial, Poisson, Geometric, Uniform, Normal, Gamma, Chi-squared (x2), Exponential, Beta, t and F distributions.
Section 2.2 reviews two methods of estimation, while section 2.3 reviews the properties of the resulting estimators. Section 2.4 gives a brief review of test of hypotheses, while section 2.5 discusses the meaning of confidence intervals. These sections are fundamental background for this book, and the reader should make sure that he or she is familiar with these concepts. Also, be sure to solve the exercises at the end of this chapter.