21 окт. 2020 г. · In other words, the expectation with respect to a distribution p(x) can be written in terms of the original distribution p(z).

16 мая 2011 г. · In general if X∼f(x) then for a function g(x) you have E(g(X))=∫g(x)f(x)dx. You can verify this for simple cases by deriving the distribution of ...

4 дек. 2012 г. · In general, the expectation of g(X) can often be approximated using a Taylor expansion around the mean; let a=E(X).

24 мар. 2015 г. · The expected value of a function f of a random variable x∈Rn is defined as Ex[f(x)]=∫p(x)f(x)dx where p() is the pdf of x.

22 февр. 2016 г. · it is convention to define 0×log(0)=0. Therefore, the integral equals −k.

22 окт. 2020 г. · I am trying to understand transforming random variables into a different distribution. I don't get how this works.

11 июл. 2021 г. · By using conditional expectation (double projection), E[g(X1,⋯,XN)h(X1,⋯,XJ)]=E[E[g(X1,⋯,XN)h(X1,⋯,XJ)|(X1,⋯,XJ)]]=E[E[g(X1,⋯,XN)|(X1,⋯ ...

6 дек. 2012 г. · The following is what I ended up using: Write σ(N(μ,s2))=σ(μ+X) where X∼N(0,s2). We can use a Taylor series expansion.

26 сент. 2021 г. · Now let S=g(X) be our transformed discrete random variable and let S≡{g(x)|x∈X} be the domain of this latter random variable.

22 мая 2021 г. · It arises from the fact that the region [y,y+ΔY] for the original random variable Y corresponds to the region [g−1(y),g−1(y+ΔY)] for the random ...