In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears 23 transformation formula.doi:10.1016/j.jmaa.2011.01.044Mingjin Wang...
The expectation of a random variable conditional on is denoted by Conditional expectation of a discrete random variableWe start with the case in which and are two discrete random variables and, considered together, they form a discrete random vector. The formula for the conditional mean of given ...
An expectation formula with applications 来自 Semantic Scholar 喜欢 0 阅读量: 36 作者: Mingjin Wang 摘要: In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an ...
Mathematically, the expectation value of a random variable X is defined as the sum of the product of each possible value of X with its corresponding probability. For a discrete random variable, theexpectation value (E[X]) is calculated using the formula: E[X] = ∑(x * P(X = x)) whe...
For a random variable that has a probability density functionp(y) mathematical expectation is defined by the formula Mathematical expectation characterizes the distribution of values of a random variable. The role of mathematical expectation is fully explained by the law of large numbers. When random...
Note that Var(X|Y=y)(X|Y=y) is a function of yy. Similar to our discussion on E[X|Y=y]E[X|Y=y] and E[X|Y]E[X|Y], we define Var(X|Y)(X|Y) as a function of the random variable YY. That is, Var(X|Y)(X|Y) is a random variable whose value equals Var(X|Y=y...
The mathematical expectation will be given by the mathematical formula as, E(X)= Σ (x1p1, x2p2,…, xnpn), where x is a random variable with the probability function, f(x), p is the probability of the occurrence, and n is the number of all possible values In the case...
On p. 202, DeGroot and Schervish derive the formula for the variance of a binomially distributed random variable: V ar(X) = npq 4 Again they prove this by summing the variances of n Bernoulli distributed random variables (using Theorem 4.3.4). But by a variation of the above approach...
(Statistics)statisticsthe sum or integral of all possible values of a random variable, or any given function of it, multiplied by the respective probabilities of the values of the variable. Symbol:E(X).E(X) is the mean of the distribution;E(X–c) =E(X)–cwherecis a constant. Also ...
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 ...