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2011 | OriginalPaper | Chapter

4. Basic Concepts and Methods of Probability Theory and Statistics

Author : Kamran Dadkhah

Published in: Foundations of Mathematical and Computational Economics

Publisher: Springer Berlin Heidelberg

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Abstract

Probability theory is the branch of mathematics that deals with random events, that is, events whose occurrence we cannot predict with certainty. Random phenomena are a feature of every sphere of natural and social existence and of life. From the genetic makeup of plants, animals, and human beings to planetary configurations, from games such as poker and backgammon to movements in financial markets, and from weather patterns to social and political events (such as elections results), we witness stochastic or random phenomena.

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Footnotes
1
The axioms of probability theory were formulated by the great Russian mathematician Andrey Nikolaevich Kolmogorov (1903–1987) and published in 1933.
 
2
We shall denote the random variable, that is, the rule that assigns a real number to a particular outcome, by the capital letter X. Every realization of this variable, that is, the particular value assigned to an outcome, shall be denoted by x i , and by x when referring to such realizations generically.
 
3
An impossible event has probability zero, but an event with probability zero may still happen. Similarly, a sure event has probability one, but an event with probability one may still fail to happen.
 
4
Some econometrics textbooks speak of x being fixed in repeated sampling. This cryptic assertion is a reference to the use of regression models in experimental sciences. Suppose you have 10 flowerpots filled with the same type of soil. In each you plant the same type of seed and water them the same amount. However, each plant is given a different amount of fertilizer x and the yield for each plant, y, is measured. You can repeat the same experiment keeping all variables affecting the growth of the plant in each pot constant. In particular, the amount of fertilizer in each pot remains constant. Such experiments have hardly anything to do with economic issues and the use of regression analysis in economics, so we speak more generally of two random variables.
 
5
For the renowned Russian mathematician, Andrei Andreyevich Markov (1856–1922), who studied and made contributions to the subject.
 
Metadata
Title
Basic Concepts and Methods of Probability Theory and Statistics
Author
Kamran Dadkhah
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-13748-8_4