User stochasticboy321

10 votes

Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $

answered Jul 7, 2016 at 7:38

9 votes

Question about the definition of Markov kernel

answered Dec 8, 2022 at 16:14

8 votes

Why can't I compress an encrypted file?

answered Feb 6 at 21:48

8 votes

Accepted

Find the number of points in $(-\infty,\infty)$ for which $x^2-x\sin x-\cos x=0.$

answered Oct 13, 2015 at 6:29

8 votes

Accepted

Proving Renyi entropy properties

answered Nov 19, 2015 at 4:31

7 votes

Accepted

Do the properties $f(x)f(y)=f(x+y)$ and $f(x) \geq 1+x$ uniquely characterise the function $f(x)=e^x$?

answered Jun 7, 2021 at 16:10

7 votes

The entropy of entropy (or how to fix an unfair die)

answered Jul 26 at 2:16

6 votes

How to perform this sum

answered Feb 12 at 0:50

6 votes

Accepted

Let $X,Y\sim N(0,1)$. Are $X^2 +Y^2$ and $X/Y$ independent?

answered Nov 13, 2015 at 1:08

6 votes

Accepted

Empirical Kullback-Leibler divergence of two time series

answered Oct 24, 2015 at 0:33

6 votes

Accepted

Integral $\int_{-\pi}^\pi e^{\sin x} \sin 4x \ dx$

answered Sep 30, 2015 at 22:47

5 votes

Accepted

Understanding the Bromwich Integral (Inverse Laplace Transform)

answered Sep 11, 2015 at 20:41

5 votes

Prove that $U=X+Y$ and $V=X/(X+Y)$ are independent

answered Oct 15, 2015 at 5:01

5 votes

Series of independent Bernoulli variables

answered Jun 18, 2016 at 5:50

5 votes

Information-theoretic Inequality

answered Feb 16 at 18:29

5 votes

Find $\lim_{n\to\infty}\left(\int _{0}^{n}\frac{\mathrm dx}{x^{x^n}}\right)^n$

answered Nov 30, 2023 at 21:05

5 votes

Accepted

Bounding an intriguing integral from above

answered Jul 29, 2021 at 17:35

5 votes

Accepted

Proving Renyi's result on the order statistics of the exponential distribution

answered Dec 30, 2021 at 4:39

5 votes

Accepted

On the definition on almost sure convergence

answered Aug 19 at 12:54

4 votes

Accepted

Can we approximate the most likely event's probability if we know the distribution's entropy?

answered Mar 16, 2022 at 19:57

4 votes

Accepted

Solving recurrence $T(n) = 2T(n^{1/2}) + O(\log\log\log(n))$

answered Apr 11, 2022 at 21:55

4 votes

Accepted

Find $\,\lim\limits_{n\to \infty}a_n\,$ such that $\,a_n=\left\lceil{\frac{2\pi}{a_{n-1}}}\right\rceil\!\cdot\!a_{n-1}-2\pi$ .

answered Dec 30, 2022 at 18:45

4 votes

Accepted

Show that $\int_0^\infty \frac{\tan^{-1} ax-\tan^{-1} x}{x}~dx = \frac{1}{2}\pi ~ \ln(a)$

answered Aug 2, 2021 at 21:09

4 votes

Accepted

Random codes in coding theory

answered Jan 26 at 0:23

4 votes

Accepted

Inequality of entropies for Bernoulli plus Gaussian

answered Feb 29 at 19:35

4 votes

Accepted

Minimizing Differential Entropy of a Gaussian Random Variable Conditioned on Sum of Gaussian and Non-Gaussian Random Variables

answered Jun 2, 2023 at 6:53

4 votes

Accepted

how to prove that $ \lim_{n \to \infty} \sum_{k=1} ^n \left( \sqrt[p] {\frac{n^p+k^{p-1}}{n^p}} -1 \right) = \frac{1}{p^2}$ for all $p \in \mathbb{R}$

answered Oct 27, 2023 at 1:37

4 votes

Accepted

Is it true that $\left(\frac{a^2+b^2+c^2}{a+b+c}\right)^{a+b+c}≥a^ab^bc^c$?

answered Jun 27, 2016 at 17:01

4 votes

Accepted

Preserving mutual information after compressing states

answered Nov 9, 2019 at 1:49

4 votes

Accepted

Understanding the meaning of seed in generating random values?

answered Dec 19, 2015 at 8:35

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325 Answers

Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $

Question about the definition of Markov kernel

Why can't I compress an encrypted file?

Find the number of points in $(-\infty,\infty)$ for which $x^2-x\sin x-\cos x=0.$

Proving Renyi entropy properties

Do the properties $f(x)f(y)=f(x+y)$ and $f(x) \geq 1+x$ uniquely characterise the function $f(x)=e^x$?

The entropy of entropy (or how to fix an unfair die)

How to perform this sum

Let $X,Y\sim N(0,1)$. Are $X^2 +Y^2$ and $X/Y$ independent?

Empirical Kullback-Leibler divergence of two time series

Integral $\int_{-\pi}^\pi e^{\sin x} \sin 4x \ dx$

Understanding the Bromwich Integral (Inverse Laplace Transform)

Prove that $U=X+Y$ and $V=X/(X+Y)$ are independent

Series of independent Bernoulli variables

Information-theoretic Inequality

Find $\lim_{n\to\infty}\left(\int _{0}^{n}\frac{\mathrm dx}{x^{x^n}}\right)^n$

Bounding an intriguing integral from above

Proving Renyi's result on the order statistics of the exponential distribution

On the definition on almost sure convergence

Can we approximate the most likely event's probability if we know the distribution's entropy?

Solving recurrence $T(n) = 2T(n^{1/2}) + O(\log\log\log(n))$

Find $\,\lim\limits_{n\to \infty}a_n\,$ such that $\,a_n=\left\lceil{\frac{2\pi}{a_{n-1}}}\right\rceil\!\cdot\!a_{n-1}-2\pi$ .

Show that $\int_0^\infty \frac{\tan^{-1} ax-\tan^{-1} x}{x}~dx = \frac{1}{2}\pi ~ \ln(a)$

Random codes in coding theory

Inequality of entropies for Bernoulli plus Gaussian

Minimizing Differential Entropy of a Gaussian Random Variable Conditioned on Sum of Gaussian and Non-Gaussian Random Variables

how to prove that $ \lim_{n \to \infty} \sum_{k=1} ^n \left( \sqrt[p] {\frac{n^p+k^{p-1}}{n^p}} -1 \right) = \frac{1}{p^2}$ for all $p \in \mathbb{R}$

Is it true that $\left(\frac{a^2+b^2+c^2}{a+b+c}\right)^{a+b+c}≥a^ab^bc^c$?

Preserving mutual information after compressing states

Understanding the meaning of seed in generating random values?