Question

Central limit theorem for independent and weakly convergent random variables

score 274 · Answer 1 · 2020-08-31 12:13:13

274

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Central limit theorem for independent and weakly convergent random variables

Published on 31 Aug 2020 - 12:13

score 46 · Answer 2 · 2020-09-01 07:22:27

46

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Limit distribution for the inverse of the sum of exponentials

Published on 01 Sep 2020 - 7:22

score 119 · Answer 3 · 2020-09-01 07:36:09

119

Views

Let $W^1, W^2, \ldots$ be i.i.d. Brownian motions, $T_1, T_2, \ldots$ be random variables converging a.s. to $t > 0$, do we have CLT for $W^n_{T_n}$?

Published on 01 Sep 2020 - 7:36

score 167 · Answer 4 · 2020-09-01 19:54:48

167

Views

Show that $\sum_{i=1}^n X_i / \sqrt{n} \Rightarrow W$ implies $EX_1^2 <\infty$ for an i.i.d. sequence $(X_i)$.

Published on 01 Sep 2020 - 19:54

score 42 · Answer 5 · 2020-09-01 20:23:17

42

Views

Solve for the asymptotic form of recursively related functions

Published on 01 Sep 2020 - 20:23

score 37 · Answer 6 · 2020-09-03 14:10:10

37

Views

Sequence of random variables: relation between convergence and joint distributions

Published on 03 Sep 2020 - 14:10

score 193 · Answer 7 · 2020-09-04 06:05:57

193

Views

Convergence of all mixed moments implies convergence in distribution?

Published on 04 Sep 2020 - 6:05

score 513 · Answer 8 · 2020-09-04 22:59:01

513

Views

Use characteristic functions to prove normal distribution of independent random variables $X$ and $Y$ , where $X+Y$ and $X-Y$are independent

Published on 04 Sep 2020 - 22:59

score 47 · Answer 9 · 2020-09-05 01:42:50

47

Views

Clarification on application of Central Limit Theorem in Example from Rice

Published on 05 Sep 2020 - 1:42

score 72 · Answer 10 · 2020-09-09 16:26:50

72

Views

Error bounds in Poisson limit theorem

Published on 09 Sep 2020 - 16:26

score 184 · Answer 11 · 2020-09-12 21:32:18

184

Views

Proving almost sure convergence for normalized gaussian series

Published on 12 Sep 2020 - 21:32

score 120 · Answer 12 · 2020-09-14 01:54:38

120

Views

If $X_n=O_P(1)$ and $Y_n=o_P(1)$, prove $X_nY_n=o_P(1)$

Published on 14 Sep 2020 - 1:54

score 119 · Answer 13 · 2026-03-27 05:59:38

119

Views

a.s limit of the maximum of a sequence of Poisson distribution

Published on 27 Mar 2026 - 5:59

score 67 · Answer 14 · 2020-09-18 18:22:20

67

Views

Approximation of functions

Published on 18 Sep 2020 - 18:22

score 195 · Answer 15 · 2020-09-29 22:58:24

195

Views

If $X_n \sim \text{Beta}(n, n)$, show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D}{\longrightarrow} N(0,1)$

Published on 29 Sep 2020 - 22:58

List Question

Central limit theorem for independent and weakly convergent random variables

Limit distribution for the inverse of the sum of exponentials

Let $W^1, W^2, \ldots$ be i.i.d. Brownian motions, $T_1, T_2, \ldots$ be random variables converging a.s. to $t > 0$, do we have CLT for $W^n_{T_n}$?

Show that $\sum_{i=1}^n X_i / \sqrt{n} \Rightarrow W$ implies $EX_1^2 <\infty$ for an i.i.d. sequence $(X_i)$.

Solve for the asymptotic form of recursively related functions

Sequence of random variables: relation between convergence and joint distributions

Convergence of all mixed moments implies convergence in distribution?

Use characteristic functions to prove normal distribution of independent random variables $X$ and $Y$ , where $X+Y$ and $X-Y$are independent

Clarification on application of Central Limit Theorem in Example from Rice

Error bounds in Poisson limit theorem

Proving almost sure convergence for normalized gaussian series

If $X_n=O_P(1)$ and $Y_n=o_P(1)$, prove $X_nY_n=o_P(1)$

a.s limit of the maximum of a sequence of Poisson distribution

Approximation of functions

If $X_n \sim \text{Beta}(n, n)$, show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D}{\longrightarrow} N(0,1)$

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