Question

If $(u_i)$ is uniformly distributed, then $\frac1n\sum_{i=1}^nf(u_i)\xrightarrow{n\to\infty}\int_{[0,\:1)^d}f\:{\rm d}\lambda^{\otimes d}$

score 32 · Answer 1 · 2026-04-01 08:59:10

32

Views

If $(u_i)$ is uniformly distributed, then $\frac1n\sum_{i=1}^nf(u_i)\xrightarrow{n\to\infty}\int_{[0,\:1)^d}f\:{\rm d}\lambda^{\otimes d}$

Published on 01 Apr 2026 - 8:59

score 69 · Answer 2 · 2022-11-24 10:58:07

69

Views

Formal proof of rejection sampling

Published on 24 Nov 2022 - 10:58

score 58 · Answer 3 · 2026-04-01 10:29:05

58

Views

Can we construct a sequence of random variables $(X_i)$ on a metric space with a given distribution such that $d(X_i,X_j)\ge\varepsilon$?

Published on 01 Apr 2026 - 10:29

score 73 · Answer 4 · 2022-11-29 14:11:12

73

Views

Why is $\sum_{i,\:j\:\in\:I}\cos(2\pi\langle k,x_i-x_j\rangle)$ small for small $k$ whenever the $x_i$ have a minimum distance to each other?

Published on 29 Nov 2022 - 14:11

score 19 · Answer 5 · 2026-03-30 22:14:25

19

Views

Volume of a sample in stratified sampling

Published on 30 Mar 2026 - 22:14

score 99 · Answer 6 · 2022-12-07 21:45:52

99

Views

Sample a specific number of elements from a list with matching probabilities

Published on 07 Dec 2022 - 21:45

score 104 · Answer 7 · 2022-12-13 19:28:07

104

Views

What's the benefit of Box-Muller method?

Published on 13 Dec 2022 - 19:28

score 30 · Answer 8 · 2022-12-15 05:18:27

30

Views

Average of a random sample drawn from two variables

Published on 15 Dec 2022 - 5:18

score 25 · Answer 9 · 2022-12-15 22:37:31

25

Views

Is it the sampling process, not the population distribution, that makes the CLT central limit theorem work?

Published on 15 Dec 2022 - 22:37

score 37 · Answer 10 · 2022-12-24 14:58:25

37

Views

Why are the marginals of this Boltzmann-Gibbs distribution distributed according to a given density?

Published on 24 Dec 2022 - 14:58

score 71 · Answer 11 · 2026-03-30 10:36:46

71

Views

Random sampling from the intersection of two hyperspheres?

Published on 30 Mar 2026 - 10:36

score 74 · Answer 12 · 2026-03-30 11:33:54

74

Views

Sampling points from a space defined by bounded inequality

Published on 30 Mar 2026 - 11:33

score 35 · Answer 13 · 2023-01-01 22:05:33

35

Views

Variance of Sample Mean using Expectations Operator

Published on 01 Jan 2023 - 22:05

score 67 · Answer 14 · 2026-03-30 22:14:29

67

Views

What is the point density of a point sampling pattern in this context?

Published on 30 Mar 2026 - 22:14

score 181 · Answer 15 · 2023-01-05 21:25:31

181

Views

What is a "Gaussian" point process?

Published on 05 Jan 2023 - 21:25

List Question

If $(u_i)$ is uniformly distributed, then $\frac1n\sum_{i=1}^nf(u_i)\xrightarrow{n\to\infty}\int_{[0,\:1)^d}f\:{\rm d}\lambda^{\otimes d}$

Formal proof of rejection sampling

Can we construct a sequence of random variables $(X_i)$ on a metric space with a given distribution such that $d(X_i,X_j)\ge\varepsilon$?

Why is $\sum_{i,\:j\:\in\:I}\cos(2\pi\langle k,x_i-x_j\rangle)$ small for small $k$ whenever the $x_i$ have a minimum distance to each other?

Volume of a sample in stratified sampling

Sample a specific number of elements from a list with matching probabilities

What's the benefit of Box-Muller method?

Average of a random sample drawn from two variables

Is it the sampling process, not the population distribution, that makes the CLT central limit theorem work?

Why are the marginals of this Boltzmann-Gibbs distribution distributed according to a given density?

Random sampling from the intersection of two hyperspheres?

Sampling points from a space defined by bounded inequality

Variance of Sample Mean using Expectations Operator

What is the point density of a point sampling pattern in this context?

What is a "Gaussian" point process?

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