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 Apr16 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 $Z$. Apr13 answered For all $\epsilon>0$ there exists $f,g$ such that $\|f\ast g\|_p>(1-\epsilon)\|f\|_1\|g\|_p$. Apr13 awarded Revival Apr13 answered Operator norm of a convolution Apr13 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. Apr13 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 Apr13 awarded Commentator Apr13 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? Apr13 awarded Revival Apr12 answered Prerequisits for Gauss-Green theorem Apr12 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 Apr12 answered If $R$ and $s$ are the range and standard deviation of a set of $n$ values, then $4\le R^2/s^2\le 2n$ Apr12 answered How to understand/remember Holder's inequality Apr12 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 $t$ ? Apr8 asked Entropy upper bound inequality for Sub-Gaussian Random Variable Apr6 awarded Teacher Apr1 answered Points of intermediate density for a measurable set Feb16 asked Bound for variance of maximum of normal random variables Dec11 awarded Caucus Oct23 awarded Popular Question