List questions from moment-generating-functions

Published on 25 Mar 2026 - 1:24

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moment generating function basics

Published on 10 May 2026 - 9:24

6.2k

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Relationship between Laplace transform and moment generating function for queue

Published on 10 May 2026 - 12:30

130

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Unique solution to an integral equation? (Moment generating function)

Published on 10 May 2026 - 14:46

84

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Distribution of Product of Arbitrary Number of Random Variables

Published on 14 Apr 2026 - 20:39

449

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Deriving the joint MGF for $U = XY + (1-X)Z$, $X \sim \text{Bernoulli}(p=1/3), Y \sim \text{Exp}(\theta = 2), Z \sim \text{Poi}(\lambda = 3)$

Published on 25 Mar 2026 - 9:43

1k

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Expected value Taylor series

Published on 01 Apr 2026 - 5:08

211

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$\mathrm{E}[e^{u X}|\mathcal{A}] = \mathrm{E}[e^{u X}|\mathcal{B}]$ implies equality of conditional distributions

Published on 25 Mar 2026 - 9:33

55

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Show that $\varphi_X(2\pi k)=\operatorname E(e^{i2\pi kX})=1 $

Published on 25 Mar 2026 - 9:38

60

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calculating probability distribution function of double integral moment

Published on 25 Mar 2026 - 9:34

418

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moment generating function vs density function of sum of two uniform rv's

Published on 25 Mar 2026 - 9:38

53

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Given kth moment determine the distribution

Published on 25 Mar 2026 - 9:34

230

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Do the derivatives of a moment generating function evaluated at 0 uniquely determine the distribution of a random variable?

Published on 25 Mar 2026 - 9:38

193

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Even moments = 0 iff $X=0$?

Published on 10 May 2026 - 15:22

68

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where is $\sum_k(-1)^k $ going in this formula?

Published on 25 Mar 2026 - 9:37

List Question

Recursive Relation to obtain a MGF

moment generating function basics

Relationship between Laplace transform and moment generating function for queue

Unique solution to an integral equation? (Moment generating function)

Distribution of Product of Arbitrary Number of Random Variables

Deriving the joint MGF for $U = XY + (1-X)Z$, $X \sim \text{Bernoulli}(p=1/3), Y \sim \text{Exp}(\theta = 2), Z \sim \text{Poi}(\lambda = 3)$

Expected value Taylor series

$\mathrm{E}[e^{u X}|\mathcal{A}] = \mathrm{E}[e^{u X}|\mathcal{B}]$ implies equality of conditional distributions

Show that $\varphi_X(2\pi k)=\operatorname E(e^{i2\pi kX})=1 $

calculating probability distribution function of double integral moment

moment generating function vs density function of sum of two uniform rv's

Given kth moment determine the distribution

Do the derivatives of a moment generating function evaluated at 0 uniquely determine the distribution of a random variable?

Even moments = 0 iff $X=0$?

where is $\sum_k(-1)^k $ going in this formula?

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