one function of two random variables

... 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 4.7 Characteristic Functions 4.8 The Laws of Large ... air-conditioning (c) With one of two choices of a stereo system (d) With one of three exterior colors , If the sample space consists of the set of all possible vehicle types, what is the number of outcomes ... Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability Mass Functions 2.5 Continuous Random Variables and Probability Density Functions 2.6 Mean...

Ngày tải lên: 31/03/2014, 16:25

... 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 ... version of Theorem 1.2 for negatively dependent random variables Theorem 1.6 Let {Xni, ≤ i ≤ kn, n ≥ 1} be an array of rowwise negatively dependent random variables and {an, n ≥ 1} a sequence of nonnegative ... 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...

Ngày tải lên: 20/06/2014, 22:20

... for the covariance of two transformed random variables by incorporating a notion of quadrant dependence and also utilizing the idea of constraining the means of the random variables To see how ... x dx 2.7 x1 If, however, one of the two functions v and w is increasing and the other one is decreasing, then inequality 2.7 is reversed With an appropriately defined random variable X see a note ... completing the proof of Theorem 3.1 8 Journal of Inequalities and Applications An Example Here we present an example that helps to compare the bounds of Gruss 13 , Zitikis , and ¨ the one of Theorem...

Ngày tải lên: 21/06/2014, 18:20

... inequality functions of associated random variables We now generalise the above results to some nonmonotonic functions of associated random variables In Section 2, we discuss some preliminaries Two ... for nonmonotonic functions of associated random variables in Section As an application, a strong law of large numbers is derived for nonmonotonic functions of associated random variables in Section ... large numbers for nonmonotonic functions of associated random variables Corollary 4.2 Let {Yn , n ≥ 1} be sequence of nonmonotonic functions of associated random variables satisfying the conditions...

Ngày tải lên: 22/06/2014, 22:20

... A small amount of PSV was as effective as 100% TC This inability restricts the usefulness of this new ventilator function Before we can be confident of the clinical advantages of TC, more hands-on ... exceed the total WOB of healthy human beings The technique of TC is also dependent on patienttriggered ventilation and trigger work is still necessary during TC This is one of the major reasons ... the lower range of overall TC support that is actually provided in clinical situations In clinical settings, because of secretions deposited inside the ETT or because of deformity of the ETT, or...

Ngày tải lên: 12/08/2014, 19:22

... controlled by two parallel pathways within the apical complex: one comprising of Baz and DaPKC and the other comprising of Pins and Gαi The localized activity of either pathway alone is sufficient ... of this early development of functional neurons, embryos are motile after the first day of development, show spontaneous twitching of the body axis and respond to touch after the second day of ... List of Figures and Tables viii Fig 3.8 The effect of cytoskeleton on LGN cortical localization 94 Fig 3.9 The effect of colchicine treatment on cortical localization of LGN 96 Fig 3.10 Effects of...

Ngày tải lên: 12/09/2015, 09:42

... effect of FMN, but not of FAD or riboflavin, has been noticed earlier [36,37] Figure shows the effect of the FMN concentration on the reconstitution of the activity of the reduced SH Addition of about ... The contents of the bottle were gently stirred at 30 °C in the dark Two controls were run also, one with 30 lM FMN instead of enzyme and the other with buffer alone After h, a sample of the solution ... rate of reduction of NAD+ (5 mM) or BV (1 mM) was measured either directly after the addition of H2/NADH or later Data are the minimal and maximal values of three measurements Experiments with two...

Ngày tải lên: 07/03/2014, 15:20

... occasion of 50th Anniversary of Department of Mathematics, Mechanics and Informatics, Vietnam National University References [1] Tran Kim Thanh, On the characterization of 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 stable degree of the Renyi’s ... δ(ε) |at − 1|2 where C is a constant independent of ε and ψ 1(t) is the characteristic function with the distribution function Ψ1 (t) respectively Proof We have +∞ |ψ(t) − ψ1 (t)| = | |ϕ(t)|z d[A(z)...

Ngày tải lên: 14/03/2014, 13:20

... 11], the authors studied the Schur-convexities of Lr (x1 ,x2 ) and Fr (x1 ,x2 ) In this paper, we establish the Schur-convexities of two types of one- parameter mean values Lr (x) and Fr (x) for ... v ∈ Λ for any x ∈ Ω Let Δ be a set of all v ∈ Λ such that the function x → φ(v,x) is a Schur-convex (Schur-concave) function Then Δ is a closed set of Λ Proof Let l ≥ 1, l ∈ N, vl ∈ Δ, v0 ∈ Λ, ... “Optimization of Schur-convex functions,” Mathematical Inequalities & Applications, vol 1, no 3, pp 319–330, 1998 [19] K Guan, “Schur-convexity of the complete elementary symmetric function, ” Journal of...

Ngày tải lên: 22/06/2014, 06:20

... determination of the Km of GlcNAc, different concentrations of GlcNAc were used in the presence of 10 mM ATP For determination of the Km of ATP, different concentrations of ATP were used in the presence of ... reagents revealed the presence of cysteine residues in or near the active site of GlcNAc kinase [14] The number of functionally relevant cysteines was quantified to two, and dithiol-modifying reagents ... ATP-binding subdomains, indicating a common structure of the ATPbinding sites of the two enzymes Interestingly, five of the six cysteines of GlcNAc kinase had an equivalent cysteine in glucokinase,...

Ngày tải lên: 08/03/2014, 10:20

... reaction is functionally important, either in regulation of enzyme activity or as a mechanism to change the oxidation state of bound cofactor There are properties of GMDs, e.g stimulation of catalytic ... growth of peaks corresponding to the anomeric resonances of the 4-keto (compound B) and gem-diol (compound C) forms of GDP-6-deoxy-d-lyxo-hexos-4-ulose (Fig 4B) On the basis of integration of the ... assign C4 of compounds B and C It is of importance that a signal corresponding to C4 of compound B was observed at dC = 208.8 p.p.m and was indicative of a carbonyl group, whereas that of compound...

Ngày tải lên: 16/03/2014, 01:20

... case of the Paley-Zygmund inequality: for any nonnegative random variable X, Pr[X > 0] ≥ (EX)2 /EX THE CHROMATIC NUMBER OF A RANDOM GRAPH 1337 Specifically, the number of k-colorings of a random ... has been in the forefront of random graph theory, motivating some of the field’s most significant developments Indeed, one of the most fascinating facts known [13] about random graphs is that for ... 0, which concludes the proof of Proposition 10 4.2 Proof of Lemma 11 If we make the linear change of variable z = (k − 1)(kx − 1) then our goal is to show that the function g : [0, (k − 1)2 ]...

Ngày tải lên: 29/03/2014, 07:20

... 171 Statement of the theorem The introduction of auxiliary random variables 172 Proof of the theorem 174 Chapter Monomial zones of local normal attraction 177 177 178 180 Zones of normal attraction ... 10 Completion of the proof of sufficiency 240 11 Proof of the necessity 241 12 Completion of the proof 243 Chapter 13 Monomial zones of integral attraction to Cramer's system of limiting tails ... 14 Completion of the proof of Theorem 11 2.2 217 15 The general case of narrow zones 218 16 The transition to Theorems 11 2.3-5 220 17 Choice of p 222 18 Completion of the proof 224 Chapter...

Ngày tải lên: 08/04/2014, 12:28

... contains no more than two R-rated movies (Shout and Mist), at least one G and one PG (Fly, Abra Cadabra, and Jealousy), and only one foreign film (Mist) 420 c The first showing of Trek will be over ... account of any specific child, nor does he or she use any method of attack 496 e Since the speaker is basing the argument on the safety of children, if there were only a few accidents and none involved ... “Honey” and “Sittin’ on the Dock of the Bay” are either and or and The Rascals appear on the list right after Otis Redding, who cannot be #3 (or he would be followed by Bobby Goldsboro), so “Honey”...

Ngày tải lên: 18/06/2014, 17:20

... sums of random variables in the domain of attraction of the normal law Qunying Wu1,2 College of Science, Guilin University of Technology, Guilin 541004, P R China Guangxi Key Laboratory of Spatial ... < ε0 < in theorem 1.1 of [12] Remark 1.4 If EX < ∞, then X is in the domain of attraction of the normal law Therefore, the class of random variables in Theorems 1.1 is of very broad range Remark ... sequence remains unknown The purpose of this article is to study and establish the ASCLT for self-normalized partial sums of random variables in the domain of attraction of the normal law, we will show...

Ngày tải lên: 20/06/2014, 21:20

... almost 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 ... the corresponding results of independent random variable sequences, there still remains much to be desired The concept of complete convergence of a sequence of random variables was introduced ... readability of the article Author details School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China College of Science, Guilin University of Technology,...

Ngày tải lên: 20/06/2014, 22:20

... 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 sequence ... strong law of large numbers for arrays of rowwise NOD random variables Corollary 2.5 Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise NOD random variables and {an, n ≥ 1} be a sequence of positive ... purpose of this article is to study the strong limit theorems for arrays of rowwise NOD random variables As an application, the Chung-type strong law of large numbers for arrays of rowwise NOD random...

Ngày tải lên: 20/06/2014, 22:20

... 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 ... normal distribution function The Proofs 2.1 Lemmas To prove theorems, we need the following lemmas Lemma 2.1 see Let {Xn , n ≥ 1} be a sequence of strongly mixing random variables with zero ... Journal of Inequalities and Applications Lemma 2.4 see Let {ξk , k ≥ 1} be a sequence of random variables, uniformly bounded below and with finite variances, and let {dk , k ≥ 1} be a sequence of...

Ngày tải lên: 21/06/2014, 05:20

... non-parametric estimate of the covariance function of a random process is often obtained by the use of a kernel function Different kernel functions have been proposed, [8] In order to favor one kernel over ... kernel function, that is, a kernel function that can be separated into one function dependent on k and one function dependent on τ Such kernels are well suited for covariance function estimation of ... optimal kernel function can be computed by solving a system of linear equations Theorem (MSE optimal kernel for a family of random processes) For a fixed τ ∈ T , the MSE optimal kernel function HxQ...

Ngày tải lên: 21/06/2014, 07:20