Distributed random

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  • (BQ) Part 1 book "Applied statistics and probability for engineers" has contents: The role of statistics in engineering, probability, discrete random variables and probability distributions, continuous random variables and probability distributions, joint probability distributions, random sampling and data description,...and other contents.

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  • (BQ) Part 1 book "A first course in probability" has contents: Combinatorial analysis, axioms of probability, conditional probability and independence, random variables, continuous random variables, jointly distributed random variables, properties of expectation.

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  • Let us consider the composed random variable η = k=1 ξk , where ξ1 , ξ2 , ... are independent identically distributed random variables and ν is a positive value random, independent of all ξk . In [1] and [2], we gave some the stabilities of the distribution function of η in the following sense: the small changes in the distribution function of ξ k only lead to the small changes in the distribution function of η. In the paper, we investigate the distribution function of η when we have the small changes of the distribution of ν. ...

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  • (BQ) Part 2 book "A first course in probability" has contents: Jointly distributed random variables, properties of expectation, limit theorems, additional topics in probability, simulation. Invite you to reference.

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  • For many random variables, the probability distribution is a specific bell-shaped curve, called the normal curve, or Gaussian curve. This is the most common and useful distribution in statistics. 1) Standard normal distribution The standard normal distribution has the probability density function as follows:

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  • Chapter 3 REFINEMENTS OF THE LIMIT THEOREMS FOR NORMAL CONVERGENCE § 1 . Introduction In this chapter we consider a sequence X 1 , X2 , . . . of independent, identically distributed random variables belonging to the domain of attraction of the normal law. As shown in § 2 .6, the X; necessarily have a finite variance a 2 .

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  • Chapter 7 RICHTER'S LOCAL THEOREMS AND BERNSTEIN'S INEQUALITY 1 . Statement of the theorems The theorems of this chapter do not have a collective character, and are related to Theorem 6 .1.1 . We shall consider a sequence of independent, identically distributed random variables XX

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  • Chapter 12 WIDE MONOMIAL ZONES OF INTEGRAL NORMAL ATTRACTION 1 . Formulation In this chapter, as before, we study the independent, identixally distributed random variables X1, X2, . . . with E (Xi) = 0, V (Xl) = 1 . We shall study the zone [0, n"] where a 6 ; we recall that this is said to be a zone of normal attraction if,

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  • Chapter 4 LOCAL LIMIT THEOREMS § 1. Formulation of the problem Suppose that the independent, identically distributed random variables X1 , X2 ,. . . . have a lattice distribution with interval h, so that the sum Zn = X1 + X2 + . . . + X„ takes values in the arithmetic progression {na + kh ; k = 0, ± 1, . . . } .

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  • Chapter 6 LIMIT THEOREMS FOR LARGE DEVIATIONS § 1 . Introduction and examples In this and succeeding chapters we shall examine the simplest problems in the theory of large deviations . Let X1 , X2 ,. . . be independent, identically distributed random variables, with E(X1) = 0

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  • Let A be an n × n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A−1 does not exceed Cn3/2 with probability close to 1. 1. Introduction Let A be an n × n matrix, whose entries are independent, identically distributed random variables. The spectral properties of such matrices, in particular invertibility, have been extensively studied (see, e.g. [M] and the survey [DS]).

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  • This chapter is of an introductory nature, its purpose being to indicate some concepts and results from the theory of probability which are used in later chapters . Most of these are contained in Chapters 1-9 of Gnedenko [47], and will therefore be cited without proof. The first section is somewhat isolated, and contains a series of results from the foundations of the theory of probability. A detailed account may be found in [76], or in Chapter I of [31] . Some of these will not be needed in the first part of the book, in which attention is confined to independent random variables ....

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  • Tham khảo sách 'probability examples c-3 random variables ii', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • Tham khảo sách 'probability examples c-4 random variables iii', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • This paper presents an attempt at building a large scale distributed composite language model that simultaneously accounts for local word lexical information, mid-range sentence syntactic structure, and long-span document semantic content under a directed Markov random field paradigm.

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  • (BQ) Part 1 book "Biostatistics" has contents: Event algebra, probability, conditional probability, independent events, random variables, frequently applied probability distributions, random vectors, regression analysis.

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  • (BQ) Part 1 book "Elementary statistics" has contents: The nature of statistics, organizing data, descriptive measures, descriptive methods in regression and correlation, probability and random variables, the normal distribution, the sampling distribution of the sample mean.

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  • Frequency distribution models tuned to words and other linguistic events can predict the number of distinct types and their frequency distribution in samples of arbitrary sizes. We conduct, for the first time, a rigorous evaluation of these models based on cross-validation and separation of training and test data. Our experiments reveal that the prediction accuracy of the models is marred by serious overfitting problems, due to violations of the random sampling assumption in corpus data. We then propose a simple pre-processing method to alleviate such non-randomness problems. ...

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  • Recent work on Conditional Random Fields (CRFs) has demonstrated the need for regularisation to counter the tendency of these models to overfit. The standard approach to regularising CRFs involves a prior distribution over the model parameters, typically requiring search over a hyperparameter space. In this paper we address the overfitting problem from a different perspective, by factoring the CRF distribution into a weighted product of individual “expert” CRF distributions. We call this model a logarithmic opinion pool (LOP) of CRFs (LOP-CRFs).

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  • We describe a novel method that extracts paraphrases from a bitext, for both the source and target languages. In order to reduce the search space, we decompose the phrase-table into sub-phrase-tables and construct separate clusters for source and target phrases. We convert the clusters into graphs, add smoothing/syntacticinformation-carrier vertices, and compute the similarity between phrases with a random walk-based measure, the commute time.

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