It presents an assumption that in a random variable X, where X has distribution function F, if X takes the value x, a random variable Y is observed, where the distribution of Y depends on x. Thus P(x, B) = P{Y ∈ BI X = x} is prescribed in the statement of the problem, ...
conditional expectation(条件期望讲义)A Conditional expectation A.1Review of conditional densities,expectations We start with the continuous case.This is sections6.6and6.8in the book.Let X,Y be continuous random variables.We defined the conditional density of X given Y to be f X,Y(x,y)f ...
Thus, we can think of g(y)=E[X|Y=y]g(y)=E[X|Y=y] as a function of the value of random variable YY. We then write g(Y)=E[X|Y].g(Y)=E[X|Y]. We use this notation to indicate that E[X|Y]E[X|Y] is a random variable whose value equals g(y)=E[X|Y=y]g(y...
Conditional expectation and martingales of random sets The aim of this paper is to present a self-contained introduction to the theory of martingales of random sets (also called `set-valued martingales' or `mul... C Hess - 《Pattern Recognition》 被引量: 26发表: 1999年 Expectation, ...
conditional expectation(条件期望讲义)A Conditional expectation A.1Review of conditional densities,expectations We start with the continuous case.This is sections6.6and6.8in the book.Let X,Y be continuous random variables.We defined the conditional density of X given Y to be f X,Y(x,y)f ...
Statistics.the summation or integration over all values of a variate of the product of the variate and its probability or its probability density. Also calledexpectation. [1830–40] Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by ...
If X is a random variable on a probability space (Ω, F,P), the conditional expectation of X with respect to a given sub σ-field F′ of F is an F′-measurable random variable whose expected value over any set in F′ is equal to the expected value of X over this set.(...
If X is a random variable with density function f(x), and if x0 is one possible value of this random variable, then for small dx, we have (5.10)P(|x−x0|⩽dx2)≈f(x0)dx This is the probability that the x will fall in a small neighborhood of x0. The neighborhood is ...
chapter5theexpectationoperator.doc,CHAPTER 5 The Expectation Operator Definition 5.1 Let be an n-D random variable with sample space SX and with pdf . Let be any function of . The expectation operator E(*) is defined as (5.1) The integral (1) is an n-D i
Notice that we used the notation for expectation, which is E(). SinceXis a Bernoulli(p) random variable, the above formula also shows us how to compute theexpected value of a Bernoulli random variable. The expected value ofX~ Bernoulli(p) is simply, p. ...