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I would like to ask the following question:

if $M$ is a $m\times n$ constant matrix and $\eta\sim\mathcal{N}(0,I)$, then does $$\mathbf{E}_{\eta\sim\mathcal{N}}\left[\frac{\lVert M\eta\rVert}{\lVert\eta\rVert}\right]$$ exist? Also, let $x\in \mathbb{R}^n_{\ne 0}$ be an arbitrary non-zero vector. Is it possible to compute the maximum (or at least to find a tight upper-bound) over all $x$, of the quantity $$\mathbf{E}_{\eta\sim\mathcal{N}}\left[\frac{\lVert M(x+\lVert x\rVert \eta)-Mx\rVert}{\lVert Mx \rVert}\right]=\lVert x\rVert\mathbf{E}_{\eta\sim\mathcal{N}}\left[\frac{\lVert M \eta\rVert}{\lVert Mx \rVert}\right]$$

Should I ask here or on Mathematics?

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    $\begingroup$ It looks on topic; but given this is not the actual question, it's not clear the extent to which you're better off asking here or there. $\endgroup$
    – Glen_b
    Oct 5, 2018 at 12:51
  • $\begingroup$ @Glen_b ok: I'll write the full question, so that it's more clear. Give me an hour, top. $\endgroup$
    – DeltaIV
    Oct 5, 2018 at 12:57
  • $\begingroup$ @Glen_b done, let me know what you think about it now. $\endgroup$
    – DeltaIV
    Oct 5, 2018 at 13:32
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    $\begingroup$ It's on topic on either site. I would guess it's a better fit on Mathematics, but as @Tim notes, you are likely to get different kinds / styles of answers between the two sites, so you should probably choose based on your preference for the style of answer that would most benefit you. $\endgroup$
    – gung - Reinstate Monica
    Oct 5, 2018 at 13:52
  • $\begingroup$ @gung question asked here. $\endgroup$
    – DeltaIV
    Oct 7, 2018 at 8:10

1 Answer 1

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Quoting our help page:

CrossValidated is for statisticians, data miners, and anyone else doing data analysis or interested in it as a discipline. If you have a question about

  • statistical analysis, applied or theoretical
  • designing experiments
  • collecting data
  • data mining
  • machine learning
  • visualizing data
  • probability theory
  • mathematical statistics
  • statistical and data-driven computing

So questions on probability theory are perfectly on topic in here, but there is overlap with the Math page and you can find many good questions and answers on probability theory up there. My impression is that usually you can expect more concise "mathy" answers ("prove that") on Math page and longer, more descriptive answers ("explain why") on CrossValidated.

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