Elementary mapping properties show that if g is a Borel function, then Z = g ( X ) is a random variable; similarly, if h is a Borel function of two variables, then Z = h ( X, Y ) is a random variable. In this chapter, we address the basic problem: Given the distribution for ...
Consider the notion of a "square-law" detector: If x is an input to the detector, then y = x2 is its output or detected value. Consider next the case where x is a random variable with probability law ...Frieden, B. RoyThe University of Arizona...
A random variable is a rule that assigns a numeric value to every possible outcome in a sample space. Random variables may be discrete or continuous in nature. A random variable is discrete if it assumes only discrete values within a specified interval.
This chapter discusses the functions of random variables. In the special case of one-dimensional vectors, Y and Z formulae determine the expectations and second-order moments of scalar functions of random variables. In the general case for finding the expectations and second-order moments of ...
Example Let be a uniform random variable on the interval , i.e., a continuous random variable with supportand probability density functionLet where is a constant. The support of iswhere we can safely ignore the fact that , because is a zero-probability event (see Continuous random variables ...
Analysis of a function of two random variables is pretty much the same as for a function of a single random variable. Suppose that you have two discrete random variables XX and YY, and suppose that Z=g(X,Y)Z=g(X,Y), where g:R2↦Rg:R2↦R. Then, if we are interested in the...
Moment generating functions possess a uniqueness property. If the moment generating functions for two random variables match one another, then the probability mass functions must be the same. In other words, the random variables describe the same probability distribution. ...
for Discrete Random Variables Bruno Caprile ITC-irst – Centro per la Ricerca Scientifica e Tecnologica I-38050 Povo, Trento Italy Abstract An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued rando...
solid mechanics & its applicationsKotulski Z, Szczepin´ski W (2010) Functions of Independent random variables. In: Error analysis with applications in engineering, vol 169. Solid mechanics and its applications. Springer, Netherlands, pp 91-105. doi:10.1007/978-90-481-3570-7_4...
title: 【概率论】3-9:多随机变量函数(Functions of Two or More Random Variables) categories: - Mathematic - Probability keywords: - Convolution - 卷积 toc: true date: 2018-03-19 10:12:34 Abstract:本文介绍多随机变量的函数 Keywords:离散多随机变量的函数,连续多随机变量的函数,卷积 ...