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Probability Theory

A Primer
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Probability Theory: A Primer 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.
Tamas Rudas is the Head of the Department of Statistics and Dean of the Faculty of Social Sciences at Eotvos Lorand University (ELTE) in Budapest. He is also the Academic Director of the TARKI Social Research Centre. His main research area is statistics and its applications in the social sciences, especially the analysis of categorical data. He has published his work in many theoretical, applied, and methodological journals, including Annals of Statistics, Journal of the Royal Statistical Society, Sociological Methodology, Communication in Statistics, Journal of Educational and Behavioral Statistics, and Quality and Quantity. Dr. Rudas is also the author of Odds Ratios in the Analysis of Contingency Tables (Sage, 1998).
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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