To understand the distortion introduced by tabs on the jet cross-section and its growth leading to bifurcation of the jet, a surface coating visualization method was developed and employed.V.S. PUGACHEVTheory of Random Functions
The characteristic function of a random variable X is defined by ΦX(ω):=E[eiωX]=∫ℝeiωxp(x)dx, where p(x) is the probability density function of X. By the definition of the Fourier transform in Chapter 1, we know that the characteristic function of X is the conjugate of the...
We start this lecture with a definition of characteristic function. Definition Let be a random variable. Let be the imaginary unit. The function defined byis called the characteristic function of . The first thing to be noted is that exists for any . This can be proved as follows:and the ...
The advantage of the characteristic function is that it is defined for all real-valued random variables. Specifically, if XX is a real-valued random variable, we can write |ejωX|=1.|ejωX|=1. Therefore, we conclude |ϕX(ω)|=|E[ejωX]|≤E[|ejωX|]≤1.|ϕX(ω)|=...
Computation of the characteristic function using numerical integration is tim... Beaulieu,C N. - 《IEEE Transactions on Communications》 被引量: 27发表: 2008年 Estimation of the Density of G Given Observations of Y=G+E We study the problem of estimating the density of a random variable G ,...
1.The numerical feature of the random variable,such as mathematic expectancy and variance,reflects the feature of distributional function;yet it is the feature function that describes the distributional function,and promises more convenience in application.随机变量的数字特征———数学期望、方差等能反映分...
1.(Mathematics)mathsa function that assigns the value 1 to the members of a given set and the value 0 to its nonmembers 2.(Statistics)statisticsa function derived from the probability distribution function that enables the distribution of the sum of given random variables to be analysed ...
In other words, the bounded function of the dis- criminator prohibits explicitly modelling p(x|y) or p(y|x) for conditional generation. Several attempts were proposed to concatenate X and Y as an augmented random variable X , and equivalently train the cGAN ...
1 The characteristic function is one of the fundamental objects in probability theory, since it uniquely characterizes the distribution of a real-valued random vector in a concise way. Its properti...
4) feature function 特征函数 1. The numerical feature of the random variable,such as mathematic expectancy and variance,reflects the feature of distributional function;yet it is thefeature functionthat describes the distributional function,and promises more convenience in application. ...