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Epiousios
  • Member for 6 years, 10 months
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16 votes
4 answers
2k views

Wondering why proof by contradiction works

7 votes
1 answer
623 views

Rigorous definition of the conditional expectations $E(X|Y=y)$ when $P(Y=y)=0$

7 votes
1 answer
226 views

Is $(X, Y)$ always absolutely continuous with respect to $P_X \otimes P_Y$?

6 votes
1 answer
120 views

What is the largest sequence of open balls around rational numbers that does not cover $\mathbb R$?

6 votes
1 answer
1k views

Two random variables are independent if all continuous and bounded transformations are uncorrelated.

5 votes
1 answer
141 views

Explicit expression for $b$ as a function of $a$ where $\log_b a = (a/b)^{1/2}$

5 votes
0 answers
191 views

When does $\mathrm{Cov}[g(X),h(X)] \ge 0$ hold for all nondecreasing $g$ and $h$ on $\mathbb R^n$?

5 votes
2 answers
547 views

How to show that any polytope $P$ is spanned by the neighboring edges of any vertex $x$?

4 votes
2 answers
176 views

Square-summability of sequence of averages

4 votes
0 answers
2k views

Understanding a Taylor expansion in probability

4 votes
1 answer
1k views

Well-definedness of Lebesgue-Integral for non-negative measurable functions

3 votes
1 answer
204 views

Are the digits of a real number i.i.d. $Unif(\{0,\ldots,9\})$?

3 votes
1 answer
198 views

Can $A\cap B$ be represented in terms of the symmetric difference?

3 votes
1 answer
231 views

What is the condition $|f(x)| \le f(|x|)$ called?

3 votes
1 answer
89 views

Does the function $f(x) = \sum_{n=1}^\infty P(|X_n| > x)$ have any special properties?

3 votes
1 answer
648 views

Generalization of Jensen's inequality

3 votes
1 answer
532 views

Show that $\mathrm{Cov}[g(X), h(X)] \ge 0$ whenever $g$ and $h$ are nondecreasing. [duplicate]

3 votes
1 answer
89 views

Does a uniform random variable contain enough randomness to generate any random vector?

3 votes
1 answer
96 views

Expectation with order statistics

2 votes
0 answers
45 views

Prove $ \int_0^t \frac{\lambda a_z}{1+\frac{p}{1-p}e^{-\int_0^z \lambda a_s ds}} dz = \log(p + (1-p)e^{\int_0^t \lambda a_s ds}) $

2 votes
0 answers
35 views

Should we expect randomly chosen random variables to be independent?

2 votes
1 answer
45 views

Which items to buy if the best one will always be stolen?

2 votes
1 answer
249 views

Are all nondecreasing $f: \mathbb R^d \to \mathbb R$ Borel-measurable?

2 votes
1 answer
131 views

Does the inverse of a unimodular matrix with entries in $\{-1,0,1\}$ again have entries in $\{-1,0,1\}$?

2 votes
2 answers
451 views

Arithmetic mean is to addition as Harmonic mean is to ...?

2 votes
1 answer
455 views

Is there an algorithm to find the edge vectors of a polytope? [duplicate]

2 votes
1 answer
556 views

What is an interpretation of the rank of a probability matrix?

2 votes
0 answers
54 views

When is the probability measure in de Finetti's theorem finitely supported?

2 votes
1 answer
126 views

Number of permutations differing in at least $d$ spots in pairwise comparisons

2 votes
0 answers
318 views

Show that if $X$ and $Y$ are independent then $E_X(g(X,Y))=E(g(X,Y)|Y).$