two binary random variables
General Random Variables
... h CHAPTER 11 General Random Variables 125 (X,Y) C y { (X,Y)ε C} Ω x Figure 11.2: Two real-valued random variables X; Y 11.4 Two random variables Let X; Y be two random variables !IR defined on ... vector of random variables X1; X2; : : : ; Xn T , and the corresponding column vector of values x1 ; x2; : : : ; xn T has a multivariate normal distribution if and only if the random variables ... : ::: If any n random variables X1 ; X2; : : : ; Xn have this moment generating function, then they are jointly normal, and we can read out the means and covariances The random variables are jointly...
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60 Complex Random Variables and Stochastic Processes
... particular class of random variables, called circular complex random variables Circularity is a type of symmetry in the distributions of the real and imaginary parts of complex random variables and ... Likewise, a collection of N complex random variables is really just a collection of 2N real random variables with some joint distribution in R2N Because these random variables have an interpretation ... the random variables themselves are complex: the χ , F , and β distributions all describe real random variables functionally dependent on complex Gaussians Let z and q be independent scalar random...
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Báo cáo "On the stability of the distribution function of the composed random variables by their index random variable " pdf
... the distribution of the composed random variables and their stabilities Dotor thesis, Hanoi 2000 [2] Tran Kim Thanh, Nguyen Huu Bao, On the geometric composed variables and the estimate of the...
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Báo cáo " Influence of laser parameters on the stationary operation of a two-mode random micro laser " pdf
... operation of two- mode random microlaser, the variation of laser parameters influences clearly on the transformation of mode photon densities With each parameter, its influence on two modes almost ... one of other mode The reason perhaps is due to the conservation of energy in the operation of two- mode random microlaser However, this result reflects the energy transformation and the complex interaction ... photon density in random laser that has been indicated in same experiments works (see [5]) At last, we hope this study method realized here will be extended to the case of multimode random microlaser...
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theory and problems of probability, random variables, and random processes - hwei p. hsu
... Chapter Random Variables 1 7 8 38 2.1 Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability Mass Functions 2.5 Continuous Random Variables ... Problems Chapter Multiple Random Variables 38 38 39 41 41 42 43 48 48 79 3.1 Introduction 3.2 Bivariate Random Variables 3.3 Joint Distribution Functions 3.4 Discrete Random Variables - Joint Probability ... Expectation, Limit Theorems 4.1 Introduction 4.2 Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables 4.5 Expectation 4.6 Moment Generating Functions...
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probability, random variables and random processes-schaum's outline
... Chapter Random Variables 1 7 8 38 2.1 Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability Mass Functions 2.5 Continuous Random Variables ... Problems Chapter Multiple Random Variables 38 38 39 41 41 42 43 48 48 79 3.1 Introduction 3.2 Bivariate Random Variables 3.3 Joint Distribution Functions 3.4 Discrete Random Variables - Joint Probability ... Expectation, Limit Theorems 4.1 Introduction 4.2 Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables 4.5 Expectation 4.6 Moment Generating Functions...
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independent and stationary sequences of random variables
... distribution of the variables X1 , X2 , , X,, More generally, if T is any set of real numbers, a family of random variables X (t), t e T, defined on (Q, R, P) is called a random process Conditions ... can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, Xnl , Xn2, , Xnkn The Xnk are said to be uniformly ... Xl+X2+ + Xn _ An Bn (2.1 3) of stationarily dependent random variables In this section we establish this result for independent random variables ; the general case is dealt with in Theorem 18...
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mcgraw-hill - probability, random variables and random processes (schaum's outlines, ocr) - 1997
... Chapter Random Variables 1 7 8 38 2.1 Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability Mass Functions 2.5 Continuous Random Variables ... Problems Chapter Multiple Random Variables 38 38 39 41 41 42 43 48 48 79 3.1 Introduction 3.2 Bivariate Random Variables 3.3 Joint Distribution Functions 3.4 Discrete Random Variables - Joint Probability ... Expectation, Limit Theorems 4.1 Introduction 4.2 Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables 4.5 Expectation 4.6 Moment Generating Functions...
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schaum's outlines - probability, random variables and random processes, 1997
... Chapter Random Variables 1 7 8 38 2.1 Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability Mass Functions 2.5 Continuous Random Variables ... Problems Chapter Multiple Random Variables 38 38 39 41 41 42 43 48 48 79 3.1 Introduction 3.2 Bivariate Random Variables 3.3 Joint Distribution Functions 3.4 Discrete Random Variables - Joint Probability ... Expectation, Limit Theorems 4.1 Introduction 4.2 Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables 4.5 Expectation 4.6 Moment Generating Functions...
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báo cáo hóa học:"Some exponential inequalities for acceptable random variables and complete convergence" docx
... presented by Yang for NA random variables and Wang et al for NOD random variables Using the exponential inequalities, we further study the complete convergence for acceptable random variables MSC(2000): ... acceptable random variables For example, Xing et al [6] consider a strictly stationary NA sequence of random variables According to the sentence above, a sequence of strictly stationary and NA random variables ... acceptable random variables and denote Sn = n Xi for each n ≥ i=1 Remark 1.1 If {Xn , n ≥ 1} is a sequence of acceptable random variables, then {−Xn , n ≥ 1} is still a sequence of acceptable random variables...
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Báo cáo toán học: " A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law" pptx
... random variables with a non-degenerate distribution function F For each n ≥ 1, the symbol S n /Vn denotes selfnormalized partial sums, where S n = n i=1 Xi , Vn = n i=1 Xi2 We say that the random ... i.i.d random variables and VarS n ∼ nl(ηn ) as n → ∞ from EX = 0, Lemma 2.1 (iii), and (13), it follows that ¯ ¯ S n − ES n nl(ηn ) d −→ N, as n → ∞, where N denotes the standard normal random ... A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law Qunying Wu1,2 College of Science, Guilin...
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Báo cáo hóa học: " A note on the complete convergence for sequences of pairwise NQD random variables" potx
... independent random variable sequences, there still remains much to be desired The concept of complete convergence of a sequence of random variables was introduced by Hsu and Robbins [8] A sequence of random ... sure convergence of summation of random variables Hsu and Robbins [8] proved that the sequence of arithmetic means of independent and identically distributed random variables converges completely ... NQD random variables with non-identically distributed are investigated The main results obtained generalize and extend the relevant result of Wu [5] for sequences of pairwise NQD random variables...
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Báo cáo hóa học: " Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen" pptx
... subcollection is NOD An array of random variables {Xni, i ≥ 1, n ≥ 1} is called rowwise NOD random variables if for every n ≥ 1, {Xni, i ≥ 1} is a sequence of NOD random variables The concept of NOD ... strong law of large numbers for arrays of rowwise negatively associated (NA) random variables A finite collection of random variables X1, X2, , Xn is said to be negatively orthant dependent (NOD) ... Proschan [3] Obviously, independent random variables are NOD Joag-Dev and Proschan [3] pointed out that NA (one can refer to Joag-Dev and Proschan [3]) random variables are NOD They also presented...
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Báo cáo hóa học: " A note on the complete convergence for arrays of dependent random variables" docx
... convergence results for independent random variables have been extended to dependent random variables by many authors The concept of negatively associated random variables was introduced by Alam ... exists An infinite family of random variables is negatively associated if every finite subfamily is negatively associated The concept of negatively dependent random variables was introduced by ... infinite family of random variables is negatively dependent if every finite subfamily is negatively dependent Chen et al [9] extended Theorem 1.2 to negatively associated random variables Theorem...
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Báo cáo hóa học: " Some exponential inequalities for acceptable random variables and complete convergence" pptx
... acceptable random variables For example, Xing et al [6] consider a strictly stationary NA sequence of random variables According to the sentence above, a sequence of strictly stationary and NA random variables ... acceptable random variables n and denote Sn = i=1 Xi for each n ≥ Remark 1.1 If {Xn, n ≥ 1} is a sequence of acceptable random variables, then {-Xn, n ≥ 1} is still a sequence of acceptable random variables ... results of Yang [9] for NA random variables and Wang et al [10] for NOD random variables In Section 3, we will study the complete convergence for acceptable random variables using the exponential...
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Báo cáo hóa học: " Research Article Almost Sure Central Limit Theorem for Product of Partial Sums of Strongly Mixing Random Variables" docx
... mixing positive random variables Theorem 1.3 Let {Xn , n ≥ 1} be a sequence of identically distributed positive strongly mixing μ > and Var X1 σ , dk and Dn as mentioned above Denote random variable ... 1.8 In order to prove Theorem 1.3 we first establish ASCLT for certain triangular arrays of n random variables In the sequel we shall use the following notation Let bk,n i k 1/i and k n 2 sk,n ... we need the following lemmas Lemma 2.1 see Let {Xn , n ≥ 1} be a sequence of strongly mixing random variables with zero mean, and let {ak,n , ≤ k ≤ n, n ≥ 1} be a triangular array of real numbers...
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Báo cáo hóa học: " Research Article A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables" potx
... Inequalities and Applications variables Consequently, the following definition is needed to define sequences of negatively dependent random variables Definition 1.2 The random variables X1 , , Xn are ... 1.3 n P Xj > xj j An infinite sequence of random variables {Xn ; n ≥ 1} is said to be ND if every finite subset X1 , , Xn is ND Definition 1.3 Random variables X1 , X2 , , Xn , n ≥ are said ... so ND is much weaker than NA Because of the wide applications of ND random variables, the notions of ND dependence of random variables have received more and more attention recently A series of...
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