URN 
etd0525110010253 
Author 
YongYuan Chen 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2009 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
zhTW.Big5 Chinese 
Title 
Introduction to Probability Theory 
Date of Defense 
20100514 
Page Count 
300 
Keyword 
Chebyshevâ€™s inequality
central limit theorem
Poisson process
Markovâ€™s inequality
multivariate normal distribution
multinomial distribution
F distribution
t distribution
chisquare 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
inclusionexclusion 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 
MeiHui Guo  chair
MongNa Lo Huang  cochair
MayRu Chen  cochair
FuChuen Chang  advisor

Files 
indicate not accessible 
Date of Submission 
20100525 