Question

Closed form expression for the expected Euclidean distance between $2$ randomly chosen lattice points among $N$ points in a rectangular region

score 200 · Answer 1 · 2020-06-08 09:42:41

200

Views

Closed form expression for the expected Euclidean distance between $2$ randomly chosen lattice points among $N$ points in a rectangular region

Published on 08 Jun 2020 - 9:42

score 400 · Answer 2 · 2026-03-29 19:51:25

400

Views

Expectation of $X \log X$ for $X \sim \mathsf{Poisson}(\lambda)$.

Published on 29 Mar 2026 - 19:51

score 82 · Answer 3 · 2026-03-26 14:34:59

82

Views

Show that when $n$ balls are thrown into $n^3$ cells, the chance that (at least) two balls will collide goes to zero as $n\to \infty$

Published on 26 Mar 2026 - 14:34

score 127 · Answer 4 · 2026-03-27 20:01:09

127

Views

kth moment of an arbitrary function

Published on 27 Mar 2026 - 20:01

score 50 · Answer 5 · 2026-04-03 02:31:41

50

Views

Does expectation inequality imply conditional expectation inequality?

Published on 03 Apr 2026 - 2:31

score 130 · Answer 6 · 2020-06-09 12:12:34

130

Views

Minimisation and expectation inequality

Published on 09 Jun 2020 - 12:12

score 231 · Answer 7 · 2020-06-09 12:40:03

231

Views

The best way to put balls into boxes

Published on 09 Jun 2020 - 12:40

score 27 · Answer 8 · 2026-03-28 16:44:19

27

Views

Determine all $\overrightarrow{a}$ for an unbiased estimator of the variance

Published on 28 Mar 2026 - 16:44

score 148 · Answer 9 · 2026-03-27 19:53:12

148

Views

Expectation of a binomial random variable raised to a non-integer power? ("non-integer moment" of a probability distribution)

Published on 27 Mar 2026 - 19:53

score 52 · Answer 10 · 2020-06-09 19:39:07

52

Views

Expectation of a Normal r.v. multiplied by a CDF

Published on 09 Jun 2020 - 19:39

score 48 · Answer 11 · 2020-06-09 20:46:00

48

Views

Minimizing $\mathbb{E}|X-r|$ and $\mathbb{E}|X-r|^2$ in terms of $r$

Published on 09 Jun 2020 - 20:46

score 235 · Answer 12 · 2020-06-09 21:18:46

235

Views

Expected number of matching pairs from a random list

Published on 09 Jun 2020 - 21:18

score 173 · Answer 13 · 2026-03-27 19:55:07

173

Views

Showing that the $r^{th}$ derivative of the moment generating function is the $r^{th}$ raw moment

Published on 27 Mar 2026 - 19:55

score 188 · Answer 14 · 2026-03-29 19:52:41

188

Views

What is the expected value of $x/(a+x)$ where $x$ follows a Poisson distribution with parameter $\lambda$ and $a > 0$?

Published on 29 Mar 2026 - 19:52

score 355 · Answer 15 · 2026-03-28 21:34:24

355

Views

Expected number of rolling a pair of dice to generate 12?

Published on 28 Mar 2026 - 21:34

List Question

Closed form expression for the expected Euclidean distance between $2$ randomly chosen lattice points among $N$ points in a rectangular region

Expectation of $X \log X$ for $X \sim \mathsf{Poisson}(\lambda)$.

Show that when $n$ balls are thrown into $n^3$ cells, the chance that (at least) two balls will collide goes to zero as $n\to \infty$

kth moment of an arbitrary function

Does expectation inequality imply conditional expectation inequality?

Minimisation and expectation inequality

The best way to put balls into boxes

Determine all $\overrightarrow{a}$ for an unbiased estimator of the variance

Expectation of a binomial random variable raised to a non-integer power? ("non-integer moment" of a probability distribution)

Expectation of a Normal r.v. multiplied by a CDF

Minimizing $\mathbb{E}|X-r|$ and $\mathbb{E}|X-r|^2$ in terms of $r$

Expected number of matching pairs from a random list

Showing that the $r^{th}$ derivative of the moment generating function is the $r^{th}$ raw moment

What is the expected value of $x/(a+x)$ where $x$ follows a Poisson distribution with parameter $\lambda$ and $a > 0$?

Expected number of rolling a pair of dice to generate 12?

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