List questions from characteristic-functions

Published on 30 Aug 2020 - 9:00

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Convergence of $(X_k+1)^2$ using characteristic functions

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Characteristic function verifying a differential equation

Published on 31 Aug 2020 - 11:22

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Theorem Cramer-Wold.

Published on 31 Aug 2020 - 21:52

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$\int_0^\alpha (F(x+u)-F(x-u))du=\frac{1}{\pi}\int_{\mathbb{R}}\frac{1-\cos(\alpha u)}{u^2}e^{-ixu}\phi(u)du$

Published on 01 Sep 2020 - 19:59

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Vector's characteristic function.

Published on 30 Mar 2026 - 16:57

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The characteristic function of a discrete random variable

Published on 03 Sep 2020 - 18:53

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

Published on 31 Mar 2026 - 14:30

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Normal distribution magic

Published on 11 Sep 2020 - 8:45

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Integral evaluation to get the characteristic function of the Gamma distribution

Published on 26 Mar 2026 - 21:12

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Proof the Inclusion-exclusion principle with a characteristic function

Published on 18 Sep 2020 - 3:41

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Preimage of product of chraccteristic function compared to preimage of function

Published on 20 Sep 2020 - 1:04

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Finding a characteristic function for a Gamma random variable

Published on 22 Sep 2020 - 21:12

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Compact operator?

Published on 27 Sep 2020 - 11:40

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probability and generating functions...motivations and analogies

Published on 26 Mar 2026 - 16:06

List Question

Bochner's theorem using Lévy's theorem

Convergence of $(X_k+1)^2$ using characteristic functions

Characteristic function verifying a differential equation

Theorem Cramer-Wold.

$\int_0^\alpha (F(x+u)-F(x-u))du=\frac{1}{\pi}\int_{\mathbb{R}}\frac{1-\cos(\alpha u)}{u^2}e^{-ixu}\phi(u)du$

Vector's characteristic function.

The characteristic function of a discrete random variable

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

Normal distribution magic

Integral evaluation to get the characteristic function of the Gamma distribution

Proof the Inclusion-exclusion principle with a characteristic function

Preimage of product of chraccteristic function compared to preimage of function

Finding a characteristic function for a Gamma random variable

Compact operator?

probability and generating functions...motivations and analogies

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