(18) can now be viewed as the quotient of two, nonzero mean Gaussian random variables.To completely parameterize this relationship, the covariante between the numerator and denominator random variables must be determined. The summation of (20) can be viewed as the inner product of a row and ...
a tool for judging the validity of the central limit theorem argument in specific applicational situations occurring in stochastic mechanics, that is, to judge the speed of convergence of the distribution of a sum (or an integral) of mutually dependent random variables to the Gaussian distribution....
In my case, actually, , but both and are exponential random variables with mean 1 (they are the magnitude squared of Gaussian RVs with mean 0 and variance 1). It is also said that Cauchy distribution has no mean and MGF, but it has a characteristic function. However, the pdf is ...
On nonuniform Gaussian approximation for random summationLet (Ω, A, P ) be a probability space and X n , n εN, be independent and identically distributed random variables, integrable in the ( s +1)-th mean ( s ≥3) with mean zero and variance 1. Let l n , n εN, be a ...
This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy "landscape" on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation...
3.8. Values of Function as Dependent Random Variables Let us find a set of values of the function 𝑓̃(𝑖)(𝜃𝑗,𝜑𝑗)f~(i)θj,φj (1) at the icosphere grid (𝜃𝑗,𝜑𝑗)θj,φj, and consider these values as a random variable 𝑋𝑖Xi distributed on the segment...