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 Yearling
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Jul
7
awarded  Yearling
Apr
16
comment Entropy upper bound inequality for Sub-Gaussian Random Variable
But that is a useless inequality because it's easy to see that $\text{Ent}(Z)\geq 0$ for any non-negative random variable $Z$.
Apr
13
answered For all $\epsilon>0$ there exists $f,g$ such that $\|f\ast g\|_p>(1-\epsilon)\|f\|_1\|g\|_p$.
Apr
13
awarded  Revival
Apr
13
answered Operator norm of a convolution
Apr
13
comment If $R$ and $s$ are the range and standard deviation of a set of $n$ values, then $4\le R^2/s^2\le 2n$
@futurebird Translating the data (adding all the data by the same constant) does not affect both variance and range. Say if the data is from $a$ to $a+R$, we could add $-a$ to all of them so that $0\leq x_i\leq R$ and the variance and the range will stay the same. This will not change the result.
Apr
13
revised If $R$ and $s$ are the range and standard deviation of a set of $n$ values, then $4\le R^2/s^2\le 2n$
deleted 73 characters in body
Apr
13
awarded  Commentator
Apr
13
comment Entropy upper bound inequality for Sub-Gaussian Random Variable
I'm still not sure with this part: You said in the beginning that we have $$\frac{\log M(t)}{t} \leq \frac{t\sigma^2}{2}+ tE[X].$$If I understand correctly, after doing the Taylor expansion, you truncate it to get that the first two terms in the expansion is less than $\frac{t\sigma^2}{2}+ tE[X]$. It seems that you are assuming the remainder part is always non-negative for all $t$. Why is this true? Or did I misunderstand some supposedly simple argument?
Apr
13
awarded  Revival
Apr
12
answered Prerequisits for Gauss-Green theorem
Apr
12
revised If $R$ and $s$ are the range and standard deviation of a set of $n$ values, then $4\le R^2/s^2\le 2n$
added 15 characters in body
Apr
12
answered If $R$ and $s$ are the range and standard deviation of a set of $n$ values, then $4\le R^2/s^2\le 2n$
Apr
12
answered How to understand/remember Hölder's inequality
Apr
12
comment Entropy upper bound inequality for Sub-Gaussian Random Variable
The line after 'Given:' should read $\log M(t) \leq \frac{t^2 \sigma^2}{2} +t E[X]$. Also, I don't quite understand the part after the Taylor expansion. How do you conclude afterwards that the truncated Taylor series is less than $\frac{\log M(t)}{t}$ for all $t$ ?
Apr
8
asked Entropy upper bound inequality for Sub-Gaussian Random Variable
Apr
6
awarded  Teacher
Apr
1
answered Points of intermediate density for a measurable set
Feb
16
asked Bound for variance of maximum of normal random variables
Dec
11
awarded  Caucus