User Nikolaos Skout

12 votes

1 answer

3k views

Convergence in law implies uniform convergence of cdf's

asked Feb 24, 2016 at 10:55

12 votes

2 answers

924 views

Proof (without use of differential calculus) that $e^{\sqrt{x}}$ is convex on $[1,+\infty)$.

asked Feb 16, 2019 at 11:21

9 votes

2 answers

126 views

If $g$ is 2 times differentiable in $[a,b]$ and $g''+g'\,g=g$ and $g(a)=g(b)=0$, prove that $g=0$.

asked May 30, 2018 at 21:47

9 votes

3 answers

2k views

Taylor polynomial: the higher the degree, the better the approximation?

asked Apr 5, 2020 at 15:25

7 votes

3 answers

164 views

Does $\frac{n}{\sum\limits_{k=1}^{n}\Big(\frac{k}{k+1}\Big)^k}$ converge?

asked Sep 3, 2018 at 16:48

6 votes

2 answers

183 views

Convergence of series $\sum\limits_{n=1}^\infty\int\limits_{1}^{+\infty}e^{-x^n}\,dx$

asked Oct 13, 2018 at 15:51

6 votes

3 answers

2k views

If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.

asked Jan 3, 2017 at 23:20

6 votes

1 answer

173 views

Help Antie evaluate Gauss curvature of a smooth surface using ruler and a protractor

asked Mar 25 at 19:55

5 votes

2 answers

236 views

Is there a matrix $A$ such that: $A^4=\begin{pmatrix}0 & 2 & -1 & 1\\ 0 & 0 & 3 &1\\ 0 & 0& 0 & 4\\ 0 & 0 & 0 & 0 \\ \end{pmatrix} ~?$

asked Dec 23, 2016 at 21:31

5 votes

1 answer

3k views

Symmetric Difference Approximation of a Measurable Set [duplicate]

asked Feb 1, 2016 at 19:00

5 votes

5 answers

256 views

Evaluate $\lim\big(\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{2n}\big)$ using sequential methods

asked Sep 28, 2018 at 0:14

5 votes

3 answers

147 views

Example of $a,~b\in G$ such that $ab\in H\leq G$ and $a^2b^2\notin H.$

asked Jan 9, 2019 at 22:39

5 votes

2 answers

131 views

Evaluate $\iint_{[0,1]^2}\frac{dxdy}{(1+x^2+y^2)^{3/2}}$

asked Apr 8, 2019 at 12:20

5 votes

3 answers

211 views

Probability of $3+3$ cards, out of $6$ cards drawn from a solitaire

asked Feb 13, 2018 at 0:29

4 votes

1 answer

97 views

A closed convex set in a separable normed space is an intersection of closed regions, defined by hyperplanes

asked Jan 6, 2018 at 14:33

4 votes

6 answers

193 views

Prove divergence of series $1-\frac{1}{3}+\frac{2}{4}-\frac{1}{5}+\frac{2}{6}-\frac{1}{7}+\ldots$

asked Apr 11, 2019 at 7:46

4 votes

1 answer

200 views

Problem of isomorphism and counting on quotient ring $\mathbb{Z}_{101}[x]/<f(x)>$

asked Jan 10, 2019 at 23:34

4 votes

1 answer

227 views

Find $f$ if $f(x)\leq x$ and $f(x+y)\leq f(x)+f(y)$ for all $x,~y\in \mathbb{R}.$

asked Jan 23, 2019 at 12:59

4 votes

5 answers

169 views

Using $ \sum_{k=0}^{\infty}\frac{(-1)^{k}}{k!}=\frac1e$ evaluate first $3$ decimal digits of $1/e$.

asked Oct 23, 2018 at 22:36

4 votes

1 answer

89 views

Prove that $\mathbb{Q}_+$ can be enumerated as $(q_n)$ such that $\lim\sqrt[n]{q_n}$ exists.

asked Oct 27, 2018 at 20:38

4 votes

1 answer

336 views

Convergence of the series $\sum a_n$ when $\sqrt[n]{a_n}\leq 1-\frac{1}{n^\alpha}$ for $0<\alpha<1$.

asked Oct 28, 2018 at 10:17

4 votes

1 answer

3k views

Convergence in probability implies Fatou's lemma?

asked Jan 29, 2016 at 13:17

4 votes

2 answers

3k views

Probability two (specific) independent Markov chains are some time at the same state

asked Feb 11, 2017 at 18:48

4 votes

6 answers

770 views

Convergence of complex series $\sum_{n=1}^{\infty}\frac{i^n}{n}$

asked Sep 23, 2017 at 17:31

4 votes

1 answer

248 views

MLE for $p$ in Geometric distribution from Exponential distribution (two methods, two results)

asked Jan 7, 2021 at 9:06

4 votes

1 answer

893 views

Customers arrive as Poisson process, while served exponentially. (Poisson process problem)

asked Aug 31, 2019 at 7:17

4 votes

1 answer

83 views

True of false? If $f$ is decreasing, then $\frac{1}{x-a}\int\limits_a^xf(t)\mathrm{d}t$ is decreasing.

asked Oct 25, 2019 at 17:37

4 votes

1 answer

82 views

If $\int_1^xf(t)\,\mathrm{d}t\leqslant f^2(x)$ for all $x\geqslant 1$, prove that $f(x)\geqslant\frac{1}{2}\,(x-1).$

asked Oct 30, 2019 at 18:03

4 votes

2 answers

193 views

Integrability of $\sin \frac1x$ on $[0,1]$ using Darboux sums

asked Nov 20, 2019 at 18:01

4 votes

1 answer

88 views

Prove $\lim_{\varepsilon\to 0^+}\frac{1}{\varepsilon}\int\limits_{X\leqslant \varepsilon}X\mathrm{d}\mathbb{P}=0$

asked Jan 25, 2020 at 20:56

Stack Exchange Network

224 Questions

Convergence in law implies uniform convergence of cdf's

Proof (without use of differential calculus) that $e^{\sqrt{x}}$ is convex on $[1,+\infty)$.

If $g$ is 2 times differentiable in $[a,b]$ and $g''+g'\,g=g$ and $g(a)=g(b)=0$, prove that $g=0$.

Taylor polynomial: the higher the degree, the better the approximation?

Does $\frac{n}{\sum\limits_{k=1}^{n}\Big(\frac{k}{k+1}\Big)^k}$ converge?

Convergence of series $\sum\limits_{n=1}^\infty\int\limits_{1}^{+\infty}e^{-x^n}\,dx$

If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.

Help Antie evaluate Gauss curvature of a smooth surface using ruler and a protractor

Is there a matrix $A$ such that: $A^4=\begin{pmatrix}0 & 2 & -1 & 1\\ 0 & 0 & 3 &1\\ 0 & 0& 0 & 4\\ 0 & 0 & 0 & 0 \\ \end{pmatrix} ~?$

Symmetric Difference Approximation of a Measurable Set [duplicate]

Evaluate $\lim\big(\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{2n}\big)$ using sequential methods

Example of $a,~b\in G$ such that $ab\in H\leq G$ and $a^2b^2\notin H.$

Evaluate $\iint_{[0,1]^2}\frac{dxdy}{(1+x^2+y^2)^{3/2}}$

Probability of $3+3$ cards, out of $6$ cards drawn from a solitaire

A closed convex set in a separable normed space is an intersection of closed regions, defined by hyperplanes

Prove divergence of series $1-\frac{1}{3}+\frac{2}{4}-\frac{1}{5}+\frac{2}{6}-\frac{1}{7}+\ldots$

Problem of isomorphism and counting on quotient ring $\mathbb{Z}_{101}[x]/<f(x)>$

Find $f$ if $f(x)\leq x$ and $f(x+y)\leq f(x)+f(y)$ for all $x,~y\in \mathbb{R}.$

Using $ \sum_{k=0}^{\infty}\frac{(-1)^{k}}{k!}=\frac1e$ evaluate first $3$ decimal digits of $1/e$.

Prove that $\mathbb{Q}_+$ can be enumerated as $(q_n)$ such that $\lim\sqrt[n]{q_n}$ exists.

Convergence of the series $\sum a_n$ when $\sqrt[n]{a_n}\leq 1-\frac{1}{n^\alpha}$ for $0<\alpha<1$.

Convergence in probability implies Fatou's lemma?

Probability two (specific) independent Markov chains are some time at the same state

Convergence of complex series $\sum_{n=1}^{\infty}\frac{i^n}{n}$

MLE for $p$ in Geometric distribution from Exponential distribution (two methods, two results)

Customers arrive as Poisson process, while served exponentially. (Poisson process problem)

True of false? If $f$ is decreasing, then $\frac{1}{x-a}\int\limits_a^xf(t)\mathrm{d}t$ is decreasing.

If $\int_1^xf(t)\,\mathrm{d}t\leqslant f^2(x)$ for all $x\geqslant 1$, prove that $f(x)\geqslant\frac{1}{2}\,(x-1).$

Integrability of $\sin \frac1x$ on $[0,1]$ using Darboux sums

Prove $\lim_{\varepsilon\to 0^+}\frac{1}{\varepsilon}\int\limits_{X\leqslant \varepsilon}X\mathrm{d}\mathbb{P}=0$