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Probability Theory
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Probability Theory
A Primer



August 2004 | 80 pages | SAGE Publications, Inc
This book intends to give a non-technical introduction to probability theory, as it is used in the social sciences. The topics covered include the concept of probability and its relation to relative frequency, the properties of probability, discrete and continuous random variables, and binomial, uniform, normal and chi-squared distributions. Readers who have taken basic college mathematics will be comfortable with this work, which frequently draws intuition and examples instead of technically involved arguments to make its points. In spite of the elementary level of discussion, the concepts of continuous random variables and distributions are carefully developed. Thus, the book prepares the reader not only for a precise understanding of sampling theory, where discrete probabilities are used, but also to a deeper understanding of most of the statistical techniques applied in social science data analysis, where continuous probability distributions are often referenced.
 
INTRODUCTION
 
WHERE DO PROBABILITIES COME FROM?
DETERMINISTIC AND STOCHASTIC MODELS

 
FREQUENTIST AND OTHER APPROACHES

 
RELATIVE FREQUENCIES

 
EXPERIMENTS WITH INFINITELY MANY OUTCOMES

 
 
PROPERTIES OF PROBABILITY
BASIC PROPERTIES

 
ADDITIVITY

 
DENSITY FUNCTIONS

 
COUNTABLE ADDITIVITY

 
 
PROBABILITY DISTRIBUTIONS AND RANDOM VARIABLES
THE DISCRETE CASE

 
THE BINOMIAL DISTRIBUTION

 
THE CONTINUOUS CASE

 
THE NORMAL DISTRIBUTION

 
THE CHI-SQUARED DISTRIBUTION

 
 
CONCLUSIONS
 
NOTES
 
REFERENCES
 
ABOUT THE AUTHOR

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