Question

Prove that $\cos^2t$ is a characteristic function

score 226 · Answer 1 · 2026-03-23 15:12:01

226

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Prove that $\cos^2t$ is a characteristic function

Published on 23 Mar 2026 - 15:12

score 294 · Answer 2 · 2026-03-22 09:19:47

294

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Use characteristic function of X. (X is a Laplace (0,1) distribution) to obtain characteristic function of the standar Cauchy distribution

Published on 22 Mar 2026 - 9:19

score 459 · Answer 3 · 2026-03-22 17:32:01

459

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calculate the integral $ \int_{-\infty}^{+\infty} \frac{e^{-itx}}{1 + t^2} dt $

Published on 22 Mar 2026 - 17:32

score 280 · Answer 4 · 2026-03-23 03:23:32

280

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$\varphi_{X+Y}(t)=\varphi_X(t) \cdot \varphi_Y(t)$, but X and Y are not independent

Published on 23 Mar 2026 - 3:23

score 271 · Answer 5 · 2026-03-26 08:03:46

271

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Characteristic function evaluated at complex number for exponential distributed random variable

Published on 26 Mar 2026 - 8:03

score 214 · Answer 6 · 2026-03-25 18:59:44

214

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Example for Lévy's continuity theorem

Published on 25 Mar 2026 - 18:59

score 82 · Answer 7 · 2026-03-23 07:27:32

82

Views

Show $\sqrt{2}{n^3}\sum_{k=1}^n kX_k \to N(0,1)$ in distribution where $P(X_k=\pm 1)=1/2$

Published on 23 Mar 2026 - 7:27

score 124 · Answer 8 · 2026-03-22 22:41:40

124

Views

Finding the weak limit of a sequence of random variables.

Published on 22 Mar 2026 - 22:41

score 130 · Answer 9 · 2026-03-23 11:45:02

130

Views

linear combination of infinitely divisible random variables II

Published on 23 Mar 2026 - 11:45

score 1.6k · Answer 10 · 2026-03-22 22:42:17

1.6k

Views

Fourier transform and characteristic function of an interval

Published on 22 Mar 2026 - 22:42

score 747 · Answer 11 · 2026-03-23 14:40:59

747

Views

Given a characteristic function find its random variable

Published on 23 Mar 2026 - 14:40

score 75 · Answer 12 · 2026-03-25 09:20:35

75

Views

Let X be$Gamma(\alpha, \lambda)$Prove $(\lambda X - \alpha)/\sqrt{\alpha} \xrightarrow{d} N(0,1)$ as $\alpha \rightarrow \infty$ and $\lambda$is fixed

Published on 25 Mar 2026 - 9:20

score 385 · Answer 13 · 2026-03-25 18:56:34

385

Views

Core of the game and shapley value

Published on 25 Mar 2026 - 18:56

score 1k · Answer 14 · 2026-03-26 03:10:50

1k

Views

Dominating function for derivative of moment generating function

Published on 26 Mar 2026 - 3:10

score 70 · Answer 15 · 2026-03-22 22:39:08

70

Views

Existance of concave balanced function

Published on 22 Mar 2026 - 22:39

List Question

Prove that $\cos^2t$ is a characteristic function

Use characteristic function of X. (X is a Laplace (0,1) distribution) to obtain characteristic function of the standar Cauchy distribution

calculate the integral $ \int_{-\infty}^{+\infty} \frac{e^{-itx}}{1 + t^2} dt $

$\varphi_{X+Y}(t)=\varphi_X(t) \cdot \varphi_Y(t)$, but X and Y are not independent

Characteristic function evaluated at complex number for exponential distributed random variable

Example for Lévy's continuity theorem

Show $\sqrt{2}{n^3}\sum_{k=1}^n kX_k \to N(0,1)$ in distribution where $P(X_k=\pm 1)=1/2$

Finding the weak limit of a sequence of random variables.

linear combination of infinitely divisible random variables II

Fourier transform and characteristic function of an interval

Given a characteristic function find its random variable

Let X be$Gamma(\alpha, \lambda)$Prove $(\lambda X - \alpha)/\sqrt{\alpha} \xrightarrow{d} N(0,1)$ as $\alpha \rightarrow \infty$ and $\lambda$is fixed

Core of the game and shapley value

Dominating function for derivative of moment generating function

Existance of concave balanced function

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