Two Functions of Two Random Variables

Part 2 of ebook "Error analysis with applications in engineering" provides readers with contents including: Chapter 5 - Two-dimensional distributions; Chapter 6 - Two-dimensional functions of independent random variables; Chapter 7 - Three-dimensional distributions; Chapter 8 - Three-dimensional functions of independent random variables; Chapter 9 - Problems described by implicit equations;...

159p giangdongdinh 28-05-2024 3 2   Download

Part 1 of ebook "Probability theory" provides readers with contents including: discrete spaces of elementary events; an arbitrary space of elementary events; random variables and distribution functions; numerical characteristics of random variables; sequences of independent trials with two outcomes; on convergence of random variables and distributions;...

333p hanlinhchi 29-08-2023 4 2   Download

(BQ) Ebook Probability and statistics for engineers and scientists (Ninth edition): Part 1 presents the following content: Introduction to statistics and data analysis, probability, random variables and probability distributions, mathematical expectation, some discrete probability distributions, some continuous probability distributions, functions of random variables (optional), fundamental sampling distributions and data descriptions, one- and two-sample estimation problems, one- and two-sample tests of hypotheses.

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In this chapter, we will focus on two random variables, but once you understand the theory for two random variables, the extension to n random variables is straightforward. We will first discuss joint distributions of discrete random variables and then extend the results to continuous random variables.

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Lecture Probability Theory - Lecture 8: One Function of Two Random Variables. Classic problem of finding the probability density function of the sum of two random variables in terms of their joint density function. Find the density function of the sum random variable Z in terms of the joint density function of its two components X and Y that may be independent or dependent of each other.

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Lecture Probability Theory - Lecture 9: Two Functions of Two Random Variables. How to find the joint probability density function of two functions of two random variables X and Y, from the joint probability density function of X and Y is discussed here. In particular, when X and Y are independent and jointly Gaussian random variables, their magnitude and phase functions are shown to be independent, whereas the independence of the magnitude and phase functions is no longer true when X and Y are correlated Gaussian random variables. As usual, all relevant density functions are derived here.

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The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the q-stripe TSP with q ≥ 1, the objective function sums the costs for traveling from one vertex to each of the next q vertices along the tour. To solve medium to large-sized instances, a metaheuristic approach is proposed. The proposed method has two main components, which are construction and improvement phases. The construction phase generates an initial solution using the Greedy Randomized Adaptive Search Procedure (GRASP).

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The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate.

17p kethamoi1 17-11-2019 20 1   Download

We present and prove two theorems about equalities for the nth moment of nonnegative integer-valued random variables. These equalities generalize the well known equality for the first moment of a nonnegative integer-valued random variable X in terms of its cumulative distribution function, or in terms of its tail distribution.

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Chapter 5 – Common probability distributions. This chapter define and explain a probability distribution; distinguish between and give examples of discrete and continuous random variables; define a probability function, state its two key properties, and determine whether a given function satisfies those properties;...

48p allbymyself_10 03-03-2016 51 2   Download

Chapter 10 Generating Functions 10.1 Generating Functions for Discrete Distributions So far we have considered in detail only the two most important attributes of a random variable, namely, the mean and the variance. We have seen how these attributes enter into the fundamental limit theorems of probability

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Chapter 11 NARROW ZONES OF NORMAL ATTRACTION 1 . Classification of narrow zones by the function h We retain the notation of the last two chapters, and record here some new terminology. The narrow zones [0, A (n)] and [ -A (n), 0], where A (n) is continuous and increasing and A (n) = o (n b),

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