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Oxford University Press | Online Resource Centre | Dougherty: Introduction to Econometrics 5e
View Econometrics-Dougherty(5th Ed).pdf from ECON MISC at University of Dar es salaam. Introduction to Econometrics FIFTH EDITION Christopher Dougherty London School of Introduction to econometrics dougherty 4th edition pdf download - Download and Read Free Online By Christopher Dougherty Introduction to Econometrics (4th Edition) publication written by well-known writer who really. Dougherty Intro+to+Econometrics+4th+ed small. Ingkar Izdibay. Download PDF. Download Full PDF Package. This paper. A short summary of this paper. 37 Full Dougherty: Introduction to Econometrics 5e. Select resources by chapter Free econometrics software package to download with an accompanying instruction manual. PowerPoint slides. Series of presentations explaining some of the key concepts in econometrics. Study guide
Introduction to econometrics dougherty 5th edition pdf download
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It is essential that you have a secure understanding of these concepts, introduction to econometrics dougherty 5th edition pdf download, and the text assumes that you have taken an introductory statistics course that has treated them in some depth. This chapter offers a brief review.
Discrete Random Variables Your intuitive notion of probability is almost certainly perfectly adequate for the purposes of this text, and so we shall skip the traditional section on pure probability theory, fascinating subject though it may be. Many people have direct experience of probability through games of chance and gambling, and their interest in what they are doing results in an amazingly high level of technical competence, usually with no formal training. We shall begin straight away with discrete random variables.
A random variable is any variable whose value cannot be predicted exactly. A discrete random variable is one that has a specific set of possible values. An example is the total score when two dice are thrown. An example of a random variable that is not discrete is the temperature in a room. It can take any one of a continuing range of values and is an example of a continuous random variable.
We shall come to these later in this review. Continuing with the example of the two dice, suppose that one of them is green and the other red. When they are thrown, there are 36 possible experimental outcomes, since the green one can be any of the numbers from 1 to 6 and the red one likewise.
The random variable defined as their sum, which we will denote X, can taken only one of 11 values — the numbers from 2 to The relationship between the experimental outcomes and introduction to econometrics dougherty 5th edition pdf download values of this random variable is illustrated in Figure R.
Outcomes in the example with two dice C. Dougherty All rights reserved. Copies may be made for personal use. Version of REVIEW: RANDOM NUMBERS AND SAMPLING THEORY 2 TABLE R. All the probabilities are given in Table R. If you add all the probabilities together, introduction to econometrics dougherty 5th edition pdf download, you get exactly 1.
This is because it is percent certain that the value must be one of the numbers from 2 to The set of all possible values of a random variable is described as the population from which it is drawn. In this case, the population is the set of numbers from 2 to Exercises R. If they have the same value, X is defined to be 0. Find the probability distribution for X. You calculate it by multiplying each possible value of the random variable by its probability and adding.
In mathematical terms, if the random variable is denoted X, its expected value is denoted E X. Let us suppose that X can take n particular values x1, x2, REVIEW: RANDOM NUMBERS AND SAMPLING THEORY 3 TABLE R. The easiest and neatest way to calculate an expected value is to use a spreadsheet.
The left half of Table R. The right half shows the working for the present example. As you can see from the table, the expected value is equal to 7. Before going any further, let us consider an even simpler example of a random variable, the number obtained when you throw just one die. Pedantic note: This is the singular of the word whose plural is dice.
Two dice, one die. Like two mice, one mie. Well, two mice, one mouse. Like two hice, one house. Peculiar language, English. Using these data to compute the expected value, you find that it is equal to 3. Thus in this case the expected value of the random variable is a number you could not obtain at all.
The expected value of a random variable is frequently described as its population mean. In the case of a random variable X, the population mean is often denoted by µX, or just µ, if there is no ambiguity. Expected Values of Functions of Discrete Random Variables Let g X be any function of X. Suppose that X can take the n different values x1 to xn, with associated probabilities p1 to pn. In the first column, you write down all the values that X can take. In the second, you write down the corresponding probabilities.
In the third, you calculate the value of the function for the corresponding value of X, introduction to econometrics dougherty 5th edition pdf download. In the fourth, you multiply columns 2 and 3.
The answer is given by the total of column 4. The right half of Table R. You might be tempted to think that this is equal to µ2, but this is not correct.
The expected value of X was shown in Table R. Thus it is not true that E X 2 is equal to µ2,which means that introduction to econometrics dougherty 5th edition pdf download have to introduction to econometrics dougherty 5th edition pdf download careful to distinguish between E X 2 and [E X ]2 the latter being E X multiplied by E Xthat is, µ2. Expected Value Rules There are three rules that we are going to use over and over again. They are virtually self-evident, and they are equally valid for discrete and continuous random variables.
REVIEW: RANDOM NUMBERS AND SAMPLING THEORY 5 Rule 1 The expected value of the sum of several variables is equal to the sum of their expected values. Rule 3 is trivial in that it follows from the definition of a constant. Although the proof of Rule 1 is quite easy, we will omit it here. Putting the three rules together, you can simplify more complicated expressions. Exercise R. Independence of Random Variables Two random variables X and Y are said to be independent if E[g X h Y ] is equal to E[g X ] E[h Y ] for any functions g X and h Y.
Independence implies, as an important special case, that E XY is equal to E X E Y. REVIEW: RANDOM NUMBERS AND SAMPLING THEORY 6 Population Variance of a Discrete Random Variable In this text there is only one function of X in which we shall take much interest, and that is its population variance, a useful measure of the dispersion of its probability distribution. It is defined as the expected value of the square of the difference between X and its mean, that is, of X — µ 2, where µ is the population mean.
It is usually denoted σ X2with the subscript being introduction to econometrics dougherty 5th edition pdf download when it is obvious that it is referring to a particular variable. We will illustrate the calculation of population variance with the example of the two dice.
We shall calculate the expected value of X — 7 2 using Table R. An extra column, X — µhas been introduced as a step in the calculation of X — µ 2. By summing the last column in Table R. Hence σ Xthe standard deviation, is equal to 5. TABLE R. The proof is a good example of the use of the expected value rules. Note: You have already calculated µ in Exercise R. Probability Density Discrete random variables are very easy to handle in that, by definition, they can take only a finite set of values.
Each of these values has a "packet" of probability associated with it, and, if you know the size of these packets, you can calculate the population mean and variance with no trouble.
The sum of the probabilities is equal to 1. This is illustrated in Figure R. X can take values from 2 to 12 and the associated probabilities are as shown.
Simple Regression Model Q1 (From the textbook 'Introductory Econometrics' by Jeffrey Wooldridge)
, time: 8:15Introduction to econometrics dougherty 5th edition pdf download
Introduction to econometrics christopher dougherty 5th edition Econometrics is the application of statistical techniques to economic models in an effort to achieve numerical results and to verify economic theorems. The objective of this course is to provide a very thorough presentation of important econometric concepts Introduction to econometrics dougherty 5th edition pdf Econometrics is the application of statistical techniques to economic models in an effort to achieve numerical results and to verify economic theorems. The objective of this course is to provide a very thorough presentation of important econometric concepts View Econometrics-Dougherty(5th Ed).pdf from ECON MISC at University of Dar es salaam. Introduction to Econometrics FIFTH EDITION Christopher Dougherty London School of
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