List questions from characteristic-functions

Published on 17 Mar 2026 - 12:27

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How to integrate $\int\mathbf 1_{(-\frac12,\frac12)}(z-w)\mathbf 1_{(-\frac12,\frac12)}(w)dw$

Published on 17 Mar 2026 - 2:36

44

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$X\sim\mathcal N(0,1)$, Why is $\Phi_X^{(j)}(0)=0$ for $j$ odd?

Published on 17 Mar 2026 - 5:46

124

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Integrating characteristic functions.

Published on 17 Mar 2026 - 12:54

612

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Prove if $E$ is a Lebesgue measurable set, there exists a continuous function $f$ differing from $\chi_{E}$ on a set of measure $< \epsilon$?

Published on 17 Mar 2026 - 9:19

194

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Probability:questions on characteristic functions

Published on 17 Mar 2026 - 5:33

294

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Rewriting a double integral with complex exponential function

Published on 17 Mar 2026 - 0:58

64

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Measure of $\chi_\mathbb{Q}(x)$?

Published on 17 Mar 2026 - 19:36

42

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Proving and visualizing $\mathbf 1_{(x,x+a]}(y) = \mathbf 1_{[y-a,y)}(x)$

Published on 16 Mar 2026 - 20:48

122

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Showing $\sum_{k\ge 0} e^{-an} \frac{(an)^k}{k!}f(\frac{k}{n}) = \Bbb{E}\left(f\left(\frac{X_1+\cdots + X_n}{n}\right)\right)$

Published on 17 Mar 2026 - 15:15

791

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Inequality on characteristic functions (probability theory)

Published on 17 Mar 2026 - 0:37

645

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properties of characteristic function

Published on 17 Mar 2026 - 9:18

1.1k

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Conditions on Poisson random variables to convergence in probability

Published on 17 Mar 2026 - 8:49

2.3k

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What is the set with characteristic function $\chi_A(x) + \chi_B(x)-\chi_A(x)\chi_B(x)$?

Published on 17 Mar 2026 - 10:08

43

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Moment-determinacy in multivariate case

Published on 25 Mar 2026 - 13:04

List Question

Characteristic function of logarithm of random variable

How to integrate $\int\mathbf 1_{(-\frac12,\frac12)}(z-w)\mathbf 1_{(-\frac12,\frac12)}(w)dw$

$X\sim\mathcal N(0,1)$, Why is $\Phi_X^{(j)}(0)=0$ for $j$ odd?

Integrating characteristic functions.

Prove if $E$ is a Lebesgue measurable set, there exists a continuous function $f$ differing from $\chi_{E}$ on a set of measure $< \epsilon$?

Probability:questions on characteristic functions

Rewriting a double integral with complex exponential function

Measure of $\chi_\mathbb{Q}(x)$?

Proving and visualizing $\mathbf 1_{(x,x+a]}(y) = \mathbf 1_{[y-a,y)}(x)$

Showing $\sum_{k\ge 0} e^{-an} \frac{(an)^k}{k!}f(\frac{k}{n}) = \Bbb{E}\left(f\left(\frac{X_1+\cdots + X_n}{n}\right)\right)$

Inequality on characteristic functions (probability theory)

properties of characteristic function

Conditions on Poisson random variables to convergence in probability

What is the set with characteristic function $\chi_A(x) + \chi_B(x)-\chi_A(x)\chi_B(x)$?

Moment-determinacy in multivariate case

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