Question

$X_1, X_2$, ... independent variables with support in [0,1] , mean $\mu\in(0,1)$, $Y_n=X_1X_2...X_n,\;\;\;n\geq1$. Study convergence of $Y_n$

score 90 · Answer 1 · 2026-03-23 06:47:57

90

Views

$X_1, X_2$, ... independent variables with support in [0,1] , mean $\mu\in(0,1)$, $Y_n=X_1X_2...X_n,\;\;\;n\geq1$. Study convergence of $Y_n$

Published on 23 Mar 2026 - 6:47

score 194 · Answer 2 · 2026-03-23 05:55:43

194

Views

weak convergence and Cumulative distribution function

Published on 23 Mar 2026 - 5:55

score 82 · Answer 3 · 2026-03-23 05:18:55

82

Views

Given two biased coins, find probability that one gets $k$ heads before the other

Published on 23 Mar 2026 - 5:18

score 84 · Answer 4 · 2026-03-23 00:07:15

84

Views

If $(W_i)_{i\in\mathbb N}$ obeys the strong law of large numbers, what can we say about $\liminf_{d\to\infty}\frac1{d^{2\alpha}}\sum_{i=1}^dW_i$?

Published on 23 Mar 2026 - 0:07

score 56 · Answer 5 · 2026-03-25 04:41:01

56

Views

Non existence of limit of Gibbs distribution

Published on 25 Mar 2026 - 4:41

score 38 · Answer 6 · 2026-03-23 13:05:17

38

Views

If $(X_i,ξ_i)$ are mutually independent, then $\text E[|d^{-1/2}\sum_{i=1}^dg'(X_i)ξ_i|^{2q}]$ is bounded by a constant only depending on $q$

Published on 23 Mar 2026 - 13:05

score 301 · Answer 7 · 2026-03-22 17:10:16

301

Views

Probability of $\limsup_n\left\{|\frac{\max_{1\leq k \leq n}X_k}{\ln(n)}-1| >\epsilon\right\}$

Published on 22 Mar 2026 - 17:10

score 412 · Answer 8 · 2026-03-22 23:36:41

412

Views

stopping time almost surely finite

Published on 22 Mar 2026 - 23:36

score 201 · Answer 9 · 2026-03-22 22:04:05

201

Views

Rigorous construction of the pointwise limit of a sequence of random variables

Published on 22 Mar 2026 - 22:04

score 124 · Answer 10 · 2026-03-23 09:27:40

124

Views

Variant of the Strong Law of Large Numbers

Published on 23 Mar 2026 - 9:27

score 213 · Answer 11 · 2026-03-22 19:56:00

213

Views

Example for Lévy's continuity theorem

Published on 22 Mar 2026 - 19:56

score 220 · Answer 12 · 2026-03-22 18:41:25

220

Views

Central limit theorem and integrability

Published on 22 Mar 2026 - 18:41

score 40 · Answer 13 · 2026-03-23 07:25:26

40

Views

Question about series convergence motivated by selecting subsets of size 3

Published on 23 Mar 2026 - 7:25

score 532 · Answer 14 · 2026-03-22 21:31:05

532

Views

General Convergence of Exponential of Function to Dirac Delta

Published on 22 Mar 2026 - 21:31

score 77 · Answer 15 · 2026-03-22 18:28:13

77

Views

weak convergence: Show that $\mathbf{P}(X_n = q) \to 0$ as $n \to \infty$ when the cdf $F$ of the limit $X$ is continuous at $q$

Published on 22 Mar 2026 - 18:28

List Question

$X_1, X_2$, ... independent variables with support in [0,1] , mean $\mu\in(0,1)$, $Y_n=X_1X_2...X_n,\;\;\;n\geq1$. Study convergence of $Y_n$

weak convergence and Cumulative distribution function

Given two biased coins, find probability that one gets $k$ heads before the other

If $(W_i)_{i\in\mathbb N}$ obeys the strong law of large numbers, what can we say about $\liminf_{d\to\infty}\frac1{d^{2\alpha}}\sum_{i=1}^dW_i$?

Non existence of limit of Gibbs distribution

If $(X_i,ξ_i)$ are mutually independent, then $\text E[|d^{-1/2}\sum_{i=1}^dg'(X_i)ξ_i|^{2q}]$ is bounded by a constant only depending on $q$

Probability of $\limsup_n\left\{|\frac{\max_{1\leq k \leq n}X_k}{\ln(n)}-1| >\epsilon\right\}$

stopping time almost surely finite

Rigorous construction of the pointwise limit of a sequence of random variables

Variant of the Strong Law of Large Numbers

Example for Lévy's continuity theorem

Central limit theorem and integrability

Question about series convergence motivated by selecting subsets of size 3

General Convergence of Exponential of Function to Dirac Delta

weak convergence: Show that $\mathbf{P}(X_n = q) \to 0$ as $n \to \infty$ when the cdf $F$ of the limit $X$ is continuous at $q$

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