Question

Moments of the distribution relating to smoothness of the characteristic function

score 122 · Answer 1 · 2026-03-21 23:15:13

122

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Moments of the distribution relating to smoothness of the characteristic function

Published on 21 Mar 2026 - 23:15

score 264 · Answer 2 · 2026-03-22 10:04:13

264

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Merging with respect to bounded uniformly continuous functions in terms of characteristic functions

Published on 22 Mar 2026 - 10:04

score 58 · Answer 3 · 2026-03-20 21:57:41

58

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Compute $I(t) = \int_{0}^{\infty} \frac{1}{2^{k/2} \Gamma(\frac{k}{2})} x^{\frac{k}{2}-1}e^{-\frac{x}{2}} e^{jxt} dx$

Published on 20 Mar 2026 - 21:57

score 90 · Answer 4 · 2026-03-21 18:11:39

90

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Compute $I = \int_{0}^{\infty} \frac{8}{\gamma^{4}} x^{3} e^{-\frac{2}{\gamma^{2}}x^{2}} e^{jxt} dx$

Published on 21 Mar 2026 - 18:11

score 497 · Answer 5 · 2026-03-25 01:41:15

497

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Largest eigenvalue of the Laplacian Matrix in an odd cycle

Published on 25 Mar 2026 - 1:41

score 62 · Answer 6 · 2026-03-21 21:25:34

62

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Let $a, b, c ∈ R$, and let $M$ be the following matrix. Prove that $(a + c)^2 − 4ac ≥ 0$.

Published on 21 Mar 2026 - 21:25

score 128 · Answer 7 · 2026-03-22 00:51:05

128

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Finding minimal polynomial with given operator

Published on 22 Mar 2026 - 0:51

score 133 · Answer 8 · 2026-03-22 12:55:40

133

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Finding the general formula for a sequence:

Published on 22 Mar 2026 - 12:55

score 90 · Answer 9 · 2026-03-22 08:40:31

90

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Techniques for Fourier Transforms in Probability Theory

Published on 22 Mar 2026 - 8:40

score 585 · Answer 10 · 2026-03-22 07:10:56

Let X and Y two independent random variables with exponential distribution of parameter a>0. U = X+ Y and V = X- Y are not independent

score 401 · Answer 11 · 2026-03-22 07:03:03

401

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If $X$ and $Y$ are iid with mean $0$ and variance $1$, and $T= \frac{X+Y}{\sqrt{ 2 }}$ has the same distribution, prove it is standard normal

Published on 22 Mar 2026 - 7:03

score 108 · Answer 12 · 2026-03-22 03:09:50

108

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Derivative of a function involving a characteristic function.

Published on 22 Mar 2026 - 3:09

score 196 · Answer 13 · 2026-03-22 08:18:19

196

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How to calculate the limit of the characteristic functions $\chi_{[0,n]}$ and $\chi_{[-n,n]}$

Published on 22 Mar 2026 - 8:18

score 177 · Answer 14 · 2026-03-22 06:47:02

177

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Find the characteristic polynomial through the induction

Published on 22 Mar 2026 - 6:47

score 43 · Answer 15 · 2026-03-22 01:46:51

43

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Z = $Y$ $X_1$ + $(1-Y)$ $X_2$. where Y is a Bernoulli random variable. Calculate characteristic function of Z

Published on 22 Mar 2026 - 1:46

List Question

Moments of the distribution relating to smoothness of the characteristic function

Merging with respect to bounded uniformly continuous functions in terms of characteristic functions

Compute $I(t) = \int_{0}^{\infty} \frac{1}{2^{k/2} \Gamma(\frac{k}{2})} x^{\frac{k}{2}-1}e^{-\frac{x}{2}} e^{jxt} dx$

Compute $I = \int_{0}^{\infty} \frac{8}{\gamma^{4}} x^{3} e^{-\frac{2}{\gamma^{2}}x^{2}} e^{jxt} dx$

Largest eigenvalue of the Laplacian Matrix in an odd cycle

Let $a, b, c ∈ R$, and let $M$ be the following matrix. Prove that $(a + c)^2 − 4ac ≥ 0$.

Finding minimal polynomial with given operator

Finding the general formula for a sequence:

Techniques for Fourier Transforms in Probability Theory

Let X and Y two independent random variables with exponential distribution of parameter a>0. U = X+ Y and V = X- Y are not independent

If $X$ and $Y$ are iid with mean $0$ and variance $1$, and $T= \frac{X+Y}{\sqrt{ 2 }}$ has the same distribution, prove it is standard normal

Derivative of a function involving a characteristic function.

How to calculate the limit of the characteristic functions $\chi_{[0,n]}$ and $\chi_{[-n,n]}$

Find the characteristic polynomial through the induction

Z = $Y$ $X_1$ + $(1-Y)$ $X_2$. where Y is a Bernoulli random variable. Calculate characteristic function of Z

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