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Results tagged with gaussian
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user 4600
Gaussian functions / distributions / processes...
2
votes
Constructive Central Limit Theorem
Did you try given $g_n$ to let $s_n=F_{s_n}^{-1}F_{g_n}(g_n)$ where $F_X$ is the c.d.f. of $X$?
- 24.8k
1
vote
Derive concentration bound for the derivative
No, $f(z)$ being sub-Gaussian does not imply that $f'(z)$ is sub-Gaussian.
An easy way to see this is to use the fact that a sub-Gaussian must have zero mean. … So $f'(1)$ is not sub-Gaussian. …
- 24.8k
3
votes
Accepted
Divergence between two random variables
Let $0<\alpha<1$ (typically $\alpha=0.05$) and choose $\varepsilon>0$ such that
$$\alpha = \mathbb P(\left |X-\mu_X\right | > \varepsilon)$$
Now let
$$f = \mathbb P(\left |Y-\mu_X\right | > \varep …
- 24.8k
21
votes
Why is the Gaussian so pervasive in mathematics?
(The sort of obvious answer from teaching statistics several times:)
The sum of two independent normal random variables is again normal, i.e., the shape of the distribution is unchanged under addition …
- 24.8k