Global ETD Search

1	Introduction to Probability Theory Chen, Yong-Yuan 25 May 2010 (has links) 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. 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

Search results

Introduction to Probability Theory