... ofrandom variables, called circular complex random variables. Circularity is a type of symmetry in the distributions ofthe real and imaginary parts of complex randomvariablesandstochastic processes, ... Leon-Garcia, A., Probability andRandomProcesses for Electrical Engineering,2nd ed.,Addison-Wesley, Reading, MA, 1994.[4] Melsa, J. and Sage, A.,An Introduction to ProbabilityandStochastic Processes, Prentice-Hall,Englewood ... Gaussian.References[1] Loeve, M., Probability Theory,D. Van Nostrand Company, New York, 1963.[2] Papoulis, A., Probability, Random Variables, andStochastic Processes, 3rd ed., McGraw-Hill,New...
... X({) = 1, 3, 5, 7, . . .}. Find P(A). Ans. 3 CHAP. 21 RANDOM VARIABLES 2.4 DISCRETE RANDOMVARIABLESANDPROBABILITY 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 ... persons is to be selected randomly from a group of 5 men and 10 women. (a) Find the probability that the committee consists of 2 men and 3 women. (b) Find the probability that the committee...
... A, B, C are said to be independent if and only if (1 SO) Schaum's Outline ofTheory and Problems of Probability, Random Variables, andRandom 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 ... INDEPENDENT EVENTS 1.53. Let A and B be events in a sample space S. Show that if A and B are independent, then so are (a) A and B, (b) A and B, and (c) A and B. (a) From Eq....
... 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 RANDOMVARIABLESANDPROBABILITY 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 ... mean and variance of the uniform r.v. X are (Prob. 2.31) CHAP. 21 RANDOM VARIABLES 2.73. A lot consisting of 100 fuses is inspected by the following procedure: Five fuses are selected randomly,...
... Large Numbers and the Central Limit Theorem 128 Solved Problems 129 Chapter 5. RandomProcesses 161 5.1 Introduction 161 5.2 RandomProcesses 161 5.3 Characterization of RandomProcesses 161 ... of RandomProcesses 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 RandomProcesses ... Theorems 122 4.1 Introduction 122 4.2 Functions of One Random Variable 122 4.3 Functions of Two RandomVariables 123 4.4 Functions of n RandomVariables 124 4.5 Expectation 125 4.6 Moment Generating...
... inequality for acceptable randomvariables generalizes and improvesthe corresponding results presented by Yang for NA randomvariablesand Wang etal. for NOD random variables. Using the exponential ... results of Yang [9] for NA random variablesand Wang et al. [10] for NOD random variables. In Section 3, we willstudy the complete convergence for acceptable randomvariables using the exponentialinequalities ... acceptable random variables. MSC(2000): 60E15, 60F15.Keywords: acceptable random variables; exponential inequality; complete conver-gence.1 IntroductionLet {Xn, n ≥ 1} be a sequence of random variables...
... presented by Yang for NA randomvariablesand Wang et al.for NOD random variables. Using the exponential inequalities, we further study thecomplete convergence for acceptable random variables. MSC(2000): ... acceptable random variables. For example, Xing et al. [6] consider a strictlystationary NA sequence of random variables. According to the sentence above, asequence of strictly stationary and NA random ... results ofYang [9] for NA randomvariablesand Wang et al. [10] for NOD random v ariables. InSection 3, we will study the complete convergence for acceptable random variables using the exponential...
... ρ-mixing random variablesand to present some results on complete convergence under some suitableconditions. Some results generalize previous known results for rowwise independent random variables. 1. ... generated by {Xi; m ≤ i ≤ n}.The ρ-mixing randomvariables were first introduced by Kolmogorov and Rozanov1. The limiting behavior of ρ-mixing randomvariables is very rich, for example, these ... Theory of Probabilityand 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,...
... mathematical models of discrete time random processes. Such processes are also called discrete time stochastic processes, information sources, and time series.Physically a random process is something ... theory.1.2 Probability Spaces andRandom Variables The basic tool for describing random phenomena is probability theory. The history of probability theory is long, fascinating, and rich (see, for example, ... by the random process. Thus in addition to the common random process model we shall also consider modeling randomprocesses by dynamical systems asconsidered in ergo dic theory.1.2 Probability...