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…
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 ...
Before looking at more examples, we would like to talk about an important property of expectation, which is linearity. Note that if XX is a random variable, any function of XX is also a random variable, so we can talk about its expected value. For example, if Y=aX+bY=aX+b, we can...
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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 ...
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...
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。
The formula for the conditional mean of given is a straightforward implementation of the above informal definition: the weights of the average are given by the conditional probability mass function of . Definition Let and be two discrete random variables. Let be the support of and let be the ...
The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) is the probability density function. For a single continuous variable it is
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters mean, mean value - an average of n numbers computed by adding some function of the numbers and dividing by some funct...