probability random variables and random processes pdf

... X({) = 1, 3, 5, 7, . . .}. Find P(A). Ans. 3 CHAP. 21 RANDOM VARIABLES 2.4 DISCRETE RANDOM VARIABLES AND PROBABILITY MASS FUNCTIONS A. Definition : Let X be a r.v. with cdf ... digits 1 and 0 randomly with probabilities 0.6 and 0.4, respectively. (a) What is the probability that two 1s and three 0s will occur in a five-digit sequence? (b) What is the probability ... and y = r sin 9 (that is, using polar coordinates), we have Thus, and 2.22. Consider a function Find the value of a such that f (x) is a pdf of a continuous r.v. X. RANDOM VARIABLES...

Ngày tải lên: 31/03/2014, 16:25

... A, B, C are said to be independent if and only if (1 SO) Schaum's Outline of Theory and Problems of Probability, Random Variables, and Random Processes Hwei P. Hsu, Ph.D. Professor ... digits 1 and 0 randomly with probabilities 0.6 and 0.4, respectively. (a) What is the probability that two 1s and three 0s will occur in a five-digit sequence? (b) What is the probability ... 2 and property 3. Since A c S, we have and by Eq. (2.31), RANDOM VARIABLES [CHAP 2 2.30. Find the mean and variance of the r.v. X of Prob. 2.20. From Prob. 2.20, the pdf...

Ngày tải lên: 08/04/2014, 12:21

... 00 U Bi = U A, for all n 2 1, and U B, = U A, = A, i=l i=l i=l i=l CHAP. 21 RANDOM VARIABLES 2.4 DISCRETE RANDOM VARIABLES AND PROBABILITY MASS FUNCTIONS A. Definition ... digits 1 and 0 randomly with probabilities 0.6 and 0.4, respectively. (a) What is the probability that two 1s and three 0s will occur in a five-digit sequence? (b) What is the probability ... called the probability mass function (pmf) of the discrete r.v. X. Properties of pdx) : The cdf FX(x) of a discrete r.v. X can be obtained by 2.5 CONTINUOUS RANDOM VARIABLES AND PROBABILITY...

Ngày tải lên: 08/04/2014, 12:29

... Large Numbers and the Central Limit Theorem 128 Solved Problems 129 Chapter 5. Random Processes 161 5.1 Introduction 161 5.2 Random Processes 161 5.3 Characterization of Random Processes 161 ... of Random Processes 162 5.5 Discrete-Parameter Markov Chains 165 5.6 Poisson Processes 169 5.7 Wiener Processes 172 Solved Problems 172 Chapter 6. Analysis and Processing of Random Processes ... Theorems 122 4.1 Introduction 122 4.2 Functions of One Random Variable 122 4.3 Functions of Two Random Variables 123 4.4 Functions of n Random Variables 124 4.5 Expectation 125 4.6 Moment Generating...

Ngày tải lên: 08/04/2014, 12:30

... ofrandom 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 stochastic processes, ... the random variables themselves are complex: the χ 2 , F, and β distributions all describe real random variables functionally dependent on complex Gaussians. Let z and q be independent scalar random ... Leon-Garcia, A., Probability and Random Processes for Electrical Engineering, 2nd ed., Addison-Wesley, Reading, MA, 1994. [4] Melsa, J. and Sage, A., An Introduction to Probability and Stochastic Processes, Prentice-Hall, Englewood...

Ngày tải lên: 25/10/2013, 02:15

Ngày tải lên: 31/03/2014, 16:25

... ρ-mixing random variables and to present some results on complete convergence under some suitable conditions. Some results generalize previous known results for rowwise independent random variables. 1. ... generated by {X i ; m ≤ i ≤ n}. The ρ-mixing random variables were first introduced by Kolmogorov and Rozanov 1. The limiting behavior of ρ-mixing random variables is very rich, for example, these ... Theory of Probability and Its Applications, vol. 2, pp. 222–227, 1960. 2 I. A. Ibragimov, “A note on the central limit theorem for dependent random variables, ” Theory of Probability and Its Applications,...

Ngày tải lên: 21/06/2014, 07:20

Ngày tải lên: 17/12/2013, 15:18

Ngày tải lên: 21/06/2014, 22:20

... inequality for acceptable random variables generalizes and improves the corresponding results presented by Yang for NA random variables and Wang et al. for NOD random variables. Using the exponential ... 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 inequalities ... acceptable random variables. MSC(2000): 60E15, 60F15. Keywords: acceptable random variables; exponential inequality; complete conver- gence. 1 Introduction Let {X n , n ≥ 1} be a sequence of random variables...

Ngày tải lên: 18/06/2014, 15:20

... 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 ... results of Yang [9] for NA random variables and Wang et al. [10] for NOD random v ariables. In Section 3, we will study the complete convergence for acceptable random variables using the exponential...

Ngày tải lên: 20/06/2014, 23:20

... patterns, aggregation and abandonment, health and disease, and social and economic interaction. The third workshop followed a more typical SFI format (Gumerman and Gell-Mann 1994). ... expla- nations or physiological descriptions on the one hand, and the soft-ware anal- ogy for understanding cognition and motivation on the other hand (Baerends 1976; Hinde 1982; Colgan 1989; ... actions and the understandings that we have built about the world, we are tempted to assume 5 Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes ...

Ngày tải lên: 14/03/2014, 21:20

... properties and design variables, by integrating knowledge from other fields such as philosophy, psychology and arts. Commonly-accepted aesthetic properties and language terms used for evaluation and ... intention is to make sure that a variety of aesthetic judgements and emotional responses are obtained not at random, but in a more controlled and exhaustive manner which exert the most impacts. Furthermore, ... object (or feature) and that of another. A number of standard good proportion exist (e.g. the golden section). Areal and volumetric refers to similar relations in the areas and volumes of objects...

Ngày tải lên: 30/03/2014, 16:20

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Ngày tải lên: 02/07/2014, 20:20

Ngày tải lên: 02/07/2014, 20:20

... covering probability, random variables, and stochastic processes is [353]. 2.1 PROBABILITY DISTRIBUTIONS AND DENSITIES 2.1.1 Distribution of a random variable In this book, we assume that random variables ... random vectors y and z , and (2.57) still holds. A similar argument applies to the random vectors y and z . Example 2.6 First consider the random variables x and y discussed in Examples 2.2 and ... the random vector x(n)=x(n)x(n  1)::: x(n  m)] T (2.118) 2 Random Vectors and Independence In this chapter, we review central concepts of probability theory,statistics, and random processes. ...

Ngày tải lên: 13/12/2013, 14:15

... composed random variable η =  ν k=1 ξ k , where ξ 1 , ξ 2 , are independent identically distributed random variables and ν is a positive value random, independent of all ξ k . In [1] and [2], ... 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 ... Physics 23 (2007) 70-74 On the stability of the distribution function of the composed random variables by their index random variable Nguyen Huu Bao ∗ Faculty of Infomation Technology, Water Resources...

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Ngày tải lên: 08/04/2014, 12:28

... nodes can also be evaluated. The mobility model used is Modified Random Waypoint [11]witheachnode’s mobility rate randomly set b etween 0 and 20 meters per sec. As we think the node in sensor networks ... Mobile Computing,T.Imielinskiand H. F. Korth, Eds., chapter 5, Kluwer Academic Publishers, Dodrecht, The Netherlands, 1996. [4] C. E. Perkins and E. M. Royer, “Ad hoc on-demand distance vector routing,” ... Wireless Sensor Networks: Architectures and Protocols, Auerbach Publications, CRC Press, Boca Raton, Fla, USA, 2004. [11] J. Yoon, M. Liu, and B. Noble, Random waypoint considered harmful,” in...

Ngày tải lên: 21/06/2014, 17:20