Title page for etd-0525110-010253


[Back to Results | New Search]

URN etd-0525110-010253
Author Yong-Yuan Chen
Author's Email Address No Public.
Statistics This thesis had been viewed 5178 times. Download 0 times.
Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Introduction to Probability Theory
Date of Defense 2010-05-14
Page Count 300
Keyword
  • Chebyshev’s inequality
  • central limit theorem
  • Poisson process
  • Markov’s inequality
  • multivariate normal distribution
  • multinomial distribution
  • F distribution
  • t distribution
  • chi-square distribution
  • lognormal distribution
  • Beta distribution
  • Cauchy distribution
  • Weibull distribution
  • gamma distribution
  • exponential distribution
  • normal distribution
  • discrete uniform distribution
  • uniform distribution
  • hypergeometric distribution
  • geometric distribution
  • negative binomial distribution
  • Poisson distribution
  • binomial distribution
  • Bernoulli distribution
  • Bayes theorem
  • theorem of total probability
  • axioms of probability
  • multinomial theorem
  • inclusion-exclusion principle
  • set
  • Abstract 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.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Mong-Na Lo Huang - co-chair
  • May-Ru Chen - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0525110-010253.pdf
  • indicate not accessible
    Date of Submission 2010-05-25

    [Back to Results | New Search]


    Browse | Search All Available ETDs

    If you have more questions or technical problems, please contact eThesys