The Expecatation of a function 一个函数的期望,首先这个函数一定是个随机变量的函数,那么其结果也是个随机变量,是随机变量就有分布,所以就有可能有期望。 举个🌰 : 一个家电制造公司制造的电器每年出现故障的比率是XX,XX是一个当前不知道的随机变量,如果我们感兴趣的是这个电器是失效前能运行多久,我们可能会...
Conditional Expectation as a Function of a Random Variable: Remember that the conditional expectation of XX given that Y=yY=y is given by E[X|Y=y]=∑xi∈RXxiPX|Y(xi|y).E[X|Y=y]=∑xi∈RXxiPX|Y(xi|y). Note that E[X|Y=y]E[X|Y=y] depends on the value of yy. In othe...
The new bounds along with Jensen's Inequality may be applied on subsets using the procedures developed by Huang, Ziemba, and Ben-Tal to yield a procedure for obtaining upper and lower bounds on the expectation of a convex function of a multivariate random variable to an arbitrary degree of ...
Theorem 4.1.1 Law of the Unconscious Statistician. Let X be a random variable, and let r be a real valued function of a real variable. If X has a continuous distribution, then if the mean exists. If…
title: 【概率论】4-1:随机变量的期望(The Expectation of a Random Variable Part I) categories: - Mathematic - Probability keywords: Expectation toc: true date: 2018-03-20 09:48:55 Abstract:本文主要介绍期望的基础之知识,第一部分介绍连续和离散随机变量的期望。
To use the latex expected value using mathbb function, you must load amssymb package \documentclass[12pt]{article}\usepackage{amssymb}...\end{document} Next, we use\mathbbfunction. Here are five examples using LaTeX to write expected value of a random variableX: ...
Best means it is the function of X with the lowest mean squared error (expected squared di↵erence between Y and prediction of Y ). It is called the Minimum Mean Square Estimate (MMSE) Theorem Let X, Y bejointly Normal random variables. Then ...
a或者叫我捷克 Or is called me Czechoslovakia[translate] aIt remains the basis for any further corrupt behavior, whether it is in business or in public administration. The origin of any act of corruption is the fact that some basic principles have become corrupt. 它其中任一进一步保持为腐败行为...
6) mathematical expectation of fuzzy random varibles 模糊随机变量的数学期望补充资料:设计洪水的期望概率 在每一年内,设计洪水被实际洪水超过的概率。它表示所设计的水利设施在水文上破坏的可能性,因此也称为破坏概率。设以x表示实际洪水,憫p表示设计频率为p的设计洪水真值xp的估计值(因此憫p亦为随机变量),则...
This chapter focuses on the expectation of random variables, particularly the expectation of elementary random variables. It presents proofs of the Lebesgue's theorem on monotone sequences and the Lebesgue's theorem on term by term integration. The chapter discusses signed measures and the Radon–Nik...