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I saw in a paper (https://www.princeton.edu/~wbialek/rome/refs/bialek+ruyter_05.pdf Eq.37) the following identity:

http://i.imgur.com/gbBEwR4.pngenter image description here

where the <.> operator refers to a population average.

No source or justification was given for this identity & they seemed to assume the reader should be familiar with it.

However, I have no idea where they got this or how to proove it....

Any help please?

Thanks!

I saw in a paper (https://www.princeton.edu/~wbialek/rome/refs/bialek+ruyter_05.pdf Eq.37) the following identity:

http://i.imgur.com/gbBEwR4.png

where the <.> operator refers to a population average.

No source or justification was given for this identity & they seemed to assume the reader should be familiar with it.

However, I have no idea where they got this or how to proove it....

Any help please?

Thanks!

I saw in a paper (https://www.princeton.edu/~wbialek/rome/refs/bialek+ruyter_05.pdf Eq.37) the following identity:

enter image description here

where the <.> operator refers to a population average.

No source or justification was given for this identity & they seemed to assume the reader should be familiar with it.

However, I have no idea where they got this or how to proove it....

Any help please?

Thanks!

Source Link

Expectation of Gaussian random vector & arbitrary function thereof?

I saw in a paper (https://www.princeton.edu/~wbialek/rome/refs/bialek+ruyter_05.pdf Eq.37) the following identity:

http://i.imgur.com/gbBEwR4.png

where the <.> operator refers to a population average.

No source or justification was given for this identity & they seemed to assume the reader should be familiar with it.

However, I have no idea where they got this or how to proove it....

Any help please?

Thanks!