List questions from moment-generating-functions

Published on 17 Dec 2023 - 18:32

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Transformation of Random variables on MGF

Published on 17 Dec 2023 - 18:32

24

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$H^1(\mathbb{R})$ function has a finite moment?

Published on 17 Dec 2023 - 21:02

38

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Second moment of a Gaussian distribution

Published on 20 Dec 2023 - 2:17

134

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Central limit theorem: negative moments

Published on 26 Mar 2026 - 11:05

91

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What did Rota mean by "one can define cumulants relative to any sequence of binomial type"?

Published on 23 Feb 2026 - 4:57

112

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Prove $\frac{e^{t_xX_1}}{\varphi(t_x)}$ is a probability density function

Published on 01 Jan 2024 - 21:41

40

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Upper bound for $\min_{x \geq 0} e^{t x} \cdot \int_0^\infty e^{-x u} f(u) du$

Published on 04 Jan 2024 - 18:23

44

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Generate three random variable to have specific coskewness

Published on 05 Jan 2024 - 20:23

91

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Joint cumulants of repeated random variables

Published on 23 Feb 2026 - 4:55

54

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$X_1,....,X_n$ i.i.d. random variables $\sim \mathcal{N}(\mu, \sigma^2 )$, $Y = (X_1-\bar{X}, ..., X_n -\bar{X})$, find MGF of Y.

Published on 19 Jan 2024 - 14:35

67

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Computing expectation of $\frac{X}{X+Y}$ using moment generating functions only

Published on 24 Jan 2024 - 11:03

46

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Moment Generating Function for a specific set of moments - what's the distribution it follows?

Published on 06 Feb 2024 - 6:14

59

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gamma distribution is to exponential distribution what ---- distribution is to Laplace distribution?

Published on 06 Feb 2024 - 20:58

90

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Prove that for all $k \in \mathbb{N}^*$, $\mathbb{P}(S \ge k) \le \dfrac{1}{2^n}\left(\dfrac{en}{k}\right)^k$

Published on 09 Feb 2024 - 6:26

List Question

Distributions convergence and standard normal random variable using characteristic functions

Transformation of Random variables on MGF

$H^1(\mathbb{R})$ function has a finite moment?

Second moment of a Gaussian distribution

Central limit theorem: negative moments

What did Rota mean by "one can define cumulants relative to any sequence of binomial type"?

Prove $\frac{e^{t_xX_1}}{\varphi(t_x)}$ is a probability density function

Upper bound for $\min_{x \geq 0} e^{t x} \cdot \int_0^\infty e^{-x u} f(u) du$

Generate three random variable to have specific coskewness

Joint cumulants of repeated random variables

$X_1,....,X_n$ i.i.d. random variables $\sim \mathcal{N}(\mu, \sigma^2 )$, $Y = (X_1-\bar{X}, ..., X_n -\bar{X})$, find MGF of Y.

Computing expectation of $\frac{X}{X+Y}$ using moment generating functions only

Moment Generating Function for a specific set of moments - what's the distribution it follows?

gamma distribution is to exponential distribution what ---- distribution is to Laplace distribution?

Prove that for all $k \in \mathbb{N}^*$, $\mathbb{P}(S \ge k) \le \dfrac{1}{2^n}\left(\dfrac{en}{k}\right)^k$

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