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Introduction to Probability Theory

In this paper, we first present the basic principles of set theory and combinatorial analysis which are the most useful tools in computing probabilities. Then, we show some important properties derived from axioms of probability. Conditional probabilities come into play not only when some partial information is available, but also as a tool to compute probabilities more easily, even when partial information is unavailable. Then, the concept of random variable and its some related properties are introduced. For univariate random variables, we introduce the basic properties of some common discrete and continuous distributions. The important properties of jointly distributed random variables are also considered. Some inequalities, the law of large numbers and the central limit theorem are discussed. Finally, we introduce additional topics the Poisson process.
Date25 May 2010
CreatorsChen, Yong-Yuan
ContributorsMong-Na Lo Huang, May-Ru Chen, Fu-Chuen Chang, Mei-Hui Guo
Source SetsNSYSU Electronic Thesis and Dissertation Archive
Detected LanguageEnglish
Rightsnot_available, Copyright information available at source archive

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