# Random variable

Xem 1-20 trên 136 kết quả Random variable
• ### Independent And Stationary Sequences Of Random Variables

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 ....

• ### Probability Examples c-3 Random variables II

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

• ### Probability Examples c-4 Random variables III

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

• ### Báo cáo "On the stability of the distribution function of the composed random variables by their index random variable "

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. ...

• ### Entropy and Information Theory

This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy chan- nels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems....

• ### Independent And Stationary Sequences Of Random Variables - Chapter 3

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 .

• ### Independent And Stationary Sequences Of Random Variables - Chapter 7

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

• ### Independent And Stationary Sequences Of Random Variables - Chapter 12

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,

• ### Independent And Stationary Sequences Of Random Variables - Chapter 4

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, . . . } .

• ### Independent And Stationary Sequences Of Random Variables - Chapter 5

Chapter 5 LIMIT THEOREMS IN Lp SPACES § 1 . Statement of the problem Consider the sequence X1 , X2 , . . . of independent random variables with the same distribution F. If F belongs to the domain of attraction of a stable law G« with exponent a, then the distribution functions Fn of the normalised sums Zn = (X1 + X2+ . . . + Xn - An)/Bn satisfy lim Fn (x) = G a (x)

• ### Independent And Stationary Sequences Of Random Variables - Chapter 6

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

• ### Independent And Stationary Sequences Of Random Variables - Chapter 9

Chapter 9 MONOMIAL ZONES OF LOCAL NORMAL A 11 RACTION 1 . Zones of normal attraction In this chapter it will be assumed that the independent random variables X; satisfy E(X;)=0, V(XX)=62 0, and that Sn = X1 + X2+ .. . +X,, Z n = Sn/ an-1 .

• ### Independent And Stationary Sequences Of Random Variables - Chapter 19

Chapter 19 EXAMPLES AND ADDENDA The separate sections of this chapter are not related to one another except in so far as they illustrate or extend the results of Chapter 18 . © 1 . The central limit theorem for homogeneous Markov chains Consider a homogeneous Markov chain with a finite number of states (labelled 1, 2, . . ., k) and transition matrix P = (p i ;) (see, for instance, Chapter III of [47] ) . If Xn is the state of the system at time n, we have the sequence of random variables X1 , X2 , . . ., Xn...

• ### Independent And Stationary Sequences Of Random Variables - Chapter 14

Chapter 14 INTEGRAL THEOREMS HOLDING ON THE WHOLE LINE 1 . Formulation In the preceding chapters we have studied theorems of a collective type concerning large deviations in zones of the form [0, 0 (n)] and [ - (n), 0], where 0 (n) = o (n 2) . The role of the linear functionals a j, bj was played by moments of the random variables XX .

• ### Independent And Stationary Sequences Of Random Variables - Chapter 15

Chapter 15 APPROXIMATION OF DISTRIBUTIONS OF SUMS OF INDEPENDENT COMPONENTS BY INFINITELY DIVISIBLE DISTRIBUTIONS 1 . Statement of the problem We here consider the general problem of the limiting behaviour of the distribution function F§ (x) of the sum (15.1 .1) of independent random variables with the same distribution F

• ### Báo cáo: On Strong Law of Large Numbers for Dependent Random Variables

Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011, Article ID 279754, 13 pages doi:10.1155/2011/279754 Research Article On Strong Law of Large Numbers for Dependent Random Variables Zhongzhi Wang Faculty of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, China Correspondence should be addressed to Zhongzhi Wang, wzz30@ahut.edu.cn Received 16 December 2010; Accepted 3 March 2011 Academic Editor: Vijay Gupta Copyright q 2011 Zhongzhi Wang.

• ### Báo cáo hóa học: " Research Article Almost Sure Central Limit Theorem for Product of Partial Sums of Strongly Mixing Random Variables"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Almost Sure Central Limit Theorem for Product of Partial Sums of Strongly Mixing Random Variables

• ### Báo cáo hóa học: " Research Article A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables

• ### Probability Examples c-2 Random variables I

This is the second book of examples from the Theory of Probability. This topic is not my favourite, however, thanks to my former colleague, Ole Jørsboe, I somehow managed to get an idea of what it is all about. The way I have treated the topic will often diverge from the more professional treatment. On the other hand, it will probably also be closer to the way of thinking which is more common among many readers, because I also had to start from scratch.