tailieunhanh - Lecture Undergraduate econometrics, 2nd edition - Chapter 2: Some basic probability concepts

In this chapter, students will be able to understand: Experiments, outcomes and random variables; the probability distribution of a random variable; expected values involving a single random variable; using joint probability density functions; the expected value of a function of several random variables: covariance and correlation; the normal distribution. | Chapter 2 Some Basic Probability Concepts Experiments Outcomes and Random Variables A random variable is a variable whose value is unknown until it is observed. The value of a random variable results from an experiment it is not perfectly predictable. A discrete random variable can take only a finite number of values which can be counted by using the positive integers. Discrete variables are also commonly used in economics to record qualitative or nonnumerical characteristics. In this role they are sometimes called dummy variables. A continuous random variable can take any real value not just whole numbers in an interval on the real number line. Slide Undergraduate Econometrics 2nd Edition -Chapter 2 The Probability Distribution of a Random Variable The values of random variables are not known until an experiment is carried out and all possible values are not equally likely. We can make probability statements about certain values occurring by specifying a probability distribution for the random variable. If event A is an outcome of an experiment then the probability of A which we write as P A is the relative frequency with which event A occurs in many repeated trials of the experiment. For any event 0 P A 1 and the total probability of all possible event is one. Probability Distributions of Discrete Random Variables When the values of a discrete random variable are listed with their chances of occurring the resulting table of outcomes is called a probability function or a probability density function. Slide Undergraduate Econometrics 2nd Edition -Chapter 2 The probability density function spreads the total of 1 unit of probability over the set of possible values that a random variable can take. Consider a discrete random variable X the number of heads obtained in a single flip of a coin. The values that X can take are x 0 1. If the coin is fair then the probability of a head occurring is . The probability density function say f x for the .