Question

Probability and average height of two lines intersecting above the x-axis

score 89 · Answer 1 · 2026-03-24 01:17:30

89

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Probability and average height of two lines intersecting above the x-axis

Published on 24 Mar 2026 - 1:17

score 211 · Answer 2 · 2026-04-14 17:22:36

211

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Conjecture: If $x_k$ are random in $(0,\pi/2)$ then expectation of $\frac{\prod_{k=1}^n\tan x_k}{\sum_{k=1}^n\tan x_k}$ is $(\pi/2)^{2n-6}$ for $n>2$.

Published on 14 Apr 2026 - 17:22

score 76 · Answer 3 · 2026-04-10 22:26:09

76

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How should I play this dice-rolling game with modifications?

Published on 10 Apr 2026 - 22:26

score 248 · Answer 4 · 2026-04-10 16:19:31

248

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Expected value - No consecutive heads sequence

Published on 10 Apr 2026 - 16:19

score 45 · Answer 5 · 2026-04-12 19:18:11

45

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Expectation of the scalar product between matrices

Published on 12 Apr 2026 - 19:18

score 194 · Answer 6 · 2026-04-16 11:04:16

194

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What is the formula for the Mode of the Log-Normal distribution followed by the Geometric Brownian Motion?

Published on 16 Apr 2026 - 11:04

score 99 · Answer 7 · 2026-04-16 12:38:21

99

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$x$ is distributed as Poisson with parameter $\lambda$, prove $\text{E}(\log(x+0.5)-\log\lambda)+0.02/\lambda>0$

Published on 16 Apr 2026 - 12:38

score 100 · Answer 8 · 2026-04-15 16:55:36

100

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Lower-bound for $E(\log((x+1)!))$?

Published on 15 Apr 2026 - 16:55

score 46 · Answer 9 · 2026-04-13 22:44:36

46

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Marginalization of the conditional expectation

Published on 13 Apr 2026 - 22:44

score 36 · Answer 10 · 2026-04-16 07:02:39

36

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Find conditions on $f,g$ $E[ \langle g(X), f(X) \rangle ] \ge \langle E[ g(X)], E[f(X)] \rangle $ (i.e., FKG inequality for multivariate functions))

Published on 16 Apr 2026 - 7:02

score 108 · Answer 11 · 2026-04-13 09:10:58

108

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Maximum of Sub-Exponential and its Tail Probability

Published on 13 Apr 2026 - 9:10

score 158 · Answer 12 · 2026-03-25 06:10:23

158

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Sub-exponential Norm of Normal Distribution

Published on 25 Mar 2026 - 6:10

score 54 · Answer 13 · 2026-04-15 22:00:02

54

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prove $E\frac{X^k}{\omega X^{2r}+\sigma}<\infty$ for $\omega,\sigma>0, k\in\{0,1,...,2r\}$, $r\in \mathbb{N}$

Published on 15 Apr 2026 - 22:00

score 49 · Answer 14 · 2026-04-16 15:07:33

49

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Find variance and expectation with given probabilities of variable values

Published on 16 Apr 2026 - 15:07

score 42 · Answer 15 · 2026-04-12 05:14:10

42

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Upper bounds for E(f(x))

Published on 12 Apr 2026 - 5:14

List Question

Probability and average height of two lines intersecting above the x-axis

Conjecture: If $x_k$ are random in $(0,\pi/2)$ then expectation of $\frac{\prod_{k=1}^n\tan x_k}{\sum_{k=1}^n\tan x_k}$ is $(\pi/2)^{2n-6}$ for $n>2$.

How should I play this dice-rolling game with modifications?

Expected value - No consecutive heads sequence

Expectation of the scalar product between matrices

What is the formula for the Mode of the Log-Normal distribution followed by the Geometric Brownian Motion?

$x$ is distributed as Poisson with parameter $\lambda$, prove $\text{E}(\log(x+0.5)-\log\lambda)+0.02/\lambda>0$

Lower-bound for $E(\log((x+1)!))$?

Marginalization of the conditional expectation

Find conditions on $f,g$ $E[ \langle g(X), f(X) \rangle ] \ge \langle E[ g(X)], E[f(X)] \rangle $ (i.e., FKG inequality for multivariate functions))

Maximum of Sub-Exponential and its Tail Probability

Sub-exponential Norm of Normal Distribution

prove $E\frac{X^k}{\omega X^{2r}+\sigma}<\infty$ for $\omega,\sigma>0, k\in\{0,1,...,2r\}$, $r\in \mathbb{N}$

Find variance and expectation with given probabilities of variable values

Upper bounds for E(f(x))

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