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Results tagged with expectation
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user 37266
9
votes
1
answer
460
views
Bounds on the expectation of $|X-Y|$ for $X,Y$ Poisson
I would have a proof of the following fact; but it's a bit clunky, and am wondering if one can get a more elegant one (and/or improve the constants). I couldn't find this anywhere, and searching prope …
- 1,372
0
votes
Bounding an expectation involving i.i.d. standard Gaussians and Rademacher
Partial progress: here is a proof for the analogous "Gaussian case" (i.e., $Z\sim N(\mathbf{0}_d, \mathbf{I}_d)$) and $n=2$. I was hoping to get some inspiration for it to handle the "Rademacher" $Z$ …
- 1,372
4
votes
2
answers
508
views
Bounding an expectation involving i.i.d. standard Gaussians and Rademacher
with the conjecture:
$\gamma$ fixed, varying $d$
$d=5$ fixed, varying $\gamma$ (fit made with SciPy, in Python)
Update 2: For $d=1$ and $n\in\{1,2,3\}$, Mathematica could compute explicitly the expectation …
- 1,372
4
votes
1
answer
394
views
Expectation of exponential of a function of independent Rademacher r.v.'s involving the erro...
Let $Z,Z'\in\{-1,1\}^n$ be two independent vectors of i.i.d. Rademacher r.v.'s, where $1\leq n \leq d$ are two integers ($d\gg 1$). I am trying to get an upper bound on
$$
\mathbb{E}_{ZZ'}\left[ \exp\ …
- 1,372