User Guilherme Salomé

31 votes

3 answers

13k views

Integral over null set is zero

asked Feb 3, 2013 at 17:59

7 votes

1 answer

3k views

$X,Y$ i.i.d., $X$ and $(X+Y)/\sqrt{2}$ have the same dist., then show that $X$ has a normal distribution

asked Jun 13, 2013 at 20:07

7 votes

4 answers

413 views

Ratio test for sequences, the other direction

asked May 2, 2016 at 18:19

6 votes

2 answers

2k views

Understanding Direct Sum

asked Aug 5, 2015 at 20:13

6 votes

2 answers

7k views

Any set with more elements than the dimension of vector space is linearly dependent

asked Aug 6, 2015 at 21:10

4 votes

4 answers

2k views

Short proof for $1-x\leq \exp(-x)$

asked Oct 8, 2015 at 20:11

3 votes

2 answers

2k views

Inequality for concave function

asked Mar 10, 2016 at 17:32

3 votes

1 answer

469 views

Rate of convergence of Riemann sum under Lipschitz

asked Sep 12, 2016 at 23:11

2 votes

1 answer

2k views

Strongly equivalent metrics are equivalent

asked Jul 30, 2015 at 21:49

2 votes

2 answers

702 views

Example of $f:\mathbb{R}\to\mathbb{R}$ injective and bounded, but with inverse not bounded or injective.

asked Aug 2, 2015 at 17:16

2 votes

1 answer

41 views

Show that $dim(X,\succeq)\leq |X^2|$ when $X$ is finite

asked Jun 26, 2015 at 17:46

2 votes

2 answers

2k views

Prove that Euclidean distance in $\mathbb{R}^n$ is a distance

asked Jul 29, 2015 at 18:36

1 vote

3 answers

593 views

Application of Fubini's Theorem to a simple function

asked Jul 30, 2015 at 13:25

1 vote

1 answer

781 views

Prove that $C(m,n)=\frac{(m+n)(m+n+1)}{2}+m$ is a bijection from $\mathbb{N}^2$ to $\mathbb{N}$ [duplicate]

asked Jul 17, 2015 at 17:27

1 vote

2 answers

862 views

Union of sets as the union of disjoint sets - Does the proof $\forall n\in \mathbb{N}$ implies the proof for infinity?

asked Nov 8, 2014 at 3:39

1 vote

2 answers

208 views

In $\mathbb{R}^2$, u orthogonal to v, v orthogonal to w => u parallel to w

asked Jan 21, 2015 at 19:15

1 vote

2 answers

455 views

$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$

asked Mar 9, 2015 at 20:12

1 vote

1 answer

153 views

3 Events, Conditional Independence

asked Aug 27, 2015 at 23:42

1 vote

1 answer

21 views

Maximum maintains order under limit in $\mathbb{R}^2_{+}$

asked Aug 30, 2015 at 22:00

1 vote

1 answer

119 views

Covariance of conditional expectation is "orthogonal"

asked Sep 16, 2015 at 20:09

1 vote

1 answer

2k views

$E(X)$ given $f_{X,Y}$

asked Sep 16, 2015 at 22:44

1 vote

1 answer

1k views

Moment generating function to distribution function

asked Sep 20, 2015 at 2:33

1 vote

2 answers

24 views

Characterization of $L^2$ convergence by $E(\cdot),V(\cdot)$

asked Sep 25, 2015 at 15:20

1 vote

0 answers

47 views

Convergence in $L_p$ does not imply "a.s." convergence

asked Sep 25, 2015 at 18:36

1 vote

2 answers

115 views

Show that $\exists q\in\mathbb{Q}:d-c>|q-\sqrt{2}|$ where $d>c\in\mathbb{R}$

asked Aug 2, 2015 at 19:36

1 vote

1 answer

41 views

Notation question $|X^2|$

asked Jun 25, 2015 at 22:36

1 vote

1 answer

240 views

Uniformly integrable for a random variable

asked Sep 2, 2016 at 21:51

0 votes

0 answers

74 views

Law of large numbers for arrays

asked Sep 9, 2016 at 19:55

0 votes

1 answer

2k views

A conditioned on B is independent of C

asked Aug 26, 2015 at 0:15

0 votes

1 answer

110 views

Conditionally independent and intersection

asked Aug 26, 2015 at 14:03

Stack Exchange Network

31 Questions

Integral over null set is zero

$X,Y$ i.i.d., $X$ and $(X+Y)/\sqrt{2}$ have the same dist., then show that $X$ has a normal distribution

Ratio test for sequences, the other direction

Understanding Direct Sum

Any set with more elements than the dimension of vector space is linearly dependent

Short proof for $1-x\leq \exp(-x)$

Inequality for concave function

Rate of convergence of Riemann sum under Lipschitz

Strongly equivalent metrics are equivalent

Example of $f:\mathbb{R}\to\mathbb{R}$ injective and bounded, but with inverse not bounded or injective.

Show that $dim(X,\succeq)\leq |X^2|$ when $X$ is finite

Prove that Euclidean distance in $\mathbb{R}^n$ is a distance

Application of Fubini's Theorem to a simple function

Prove that $C(m,n)=\frac{(m+n)(m+n+1)}{2}+m$ is a bijection from $\mathbb{N}^2$ to $\mathbb{N}$ [duplicate]

Union of sets as the union of disjoint sets - Does the proof $\forall n\in \mathbb{N}$ implies the proof for infinity?

In $\mathbb{R}^2$, u orthogonal to v, v orthogonal to w => u parallel to w

$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$

3 Events, Conditional Independence

Maximum maintains order under limit in $\mathbb{R}^2_{+}$

Covariance of conditional expectation is "orthogonal"

$E(X)$ given $f_{X,Y}$

Moment generating function to distribution function

Characterization of $L^2$ convergence by $E(\cdot),V(\cdot)$

Convergence in $L_p$ does not imply "a.s." convergence

Show that $\exists q\in\mathbb{Q}:d-c>|q-\sqrt{2}|$ where $d>c\in\mathbb{R}$

Notation question $|X^2|$

Uniformly integrable for a random variable

Law of large numbers for arrays

A conditioned on B is independent of C

Conditionally independent and intersection