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Showing if $\frac{X}{c}\sim\text{Gamma}(a,b)$ then $X\sim\text{Gamma}(a,cb)$

score 99 · Answer 1 · 2026-03-24 19:54:56

99

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Showing if $\frac{X}{c}\sim\text{Gamma}(a,b)$ then $X\sim\text{Gamma}(a,cb)$

Published on 24 Mar 2026 - 19:54

score 88 · Answer 2 · 2026-03-24 07:18:25

88

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PDF for Moment Generating Function $(1 +\beta t)^{-\alpha}$ when $\beta > 0$

Published on 24 Mar 2026 - 7:18

score 68 · Answer 3 · 2026-03-24 12:55:28

68

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Simplify and compute the MGF of $[1-(1-(1-e^{-ax})^{N_1})(1-(1-e^{-ax})^{N_2})]^{M-1} $

Published on 24 Mar 2026 - 12:55

score 75 · Answer 4 · 2026-03-24 08:35:04

How to simplify $\sum _{l=1} ^{k} \sum_{j_1 \ge 1} \cdots \sum_{j_l \ge 1, j_1 + \cdots + j_l=k} \binom{k}{j_1 \cdots j_l} \binom{-2}{l} 2^l$

score 57 · Answer 5 · 2026-03-24 06:52:47

57

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Existence of the MGF of $X_2$

Published on 24 Mar 2026 - 6:52

score 144 · Answer 6 · 2026-03-23 16:17:34

144

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Moment Generating function with Poisson and Exponential distributed variables

Published on 23 Mar 2026 - 16:17

score 563 · Answer 7 · 2026-03-24 15:51:41

563

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Linear combination of power law distributions

Published on 24 Mar 2026 - 15:51

score 32 · Answer 8 · 2026-03-25 07:46:20

32

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The moments of the sum of variables following standard normal distribution divided by the sum of the squares of them

Published on 25 Mar 2026 - 7:46

score 12.2k · Answer 9 · 2026-03-24 03:24:54

12.2k

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Finding a Joint Moment Generating Function

Published on 24 Mar 2026 - 3:24

score 113 · Answer 10 · 2026-03-23 16:48:47

113

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Find the first moment of a probability distribution governed by a nonlinear first order ODE

Published on 23 Mar 2026 - 16:48

score 1.2k · Answer 11 · 2026-03-24 13:03:29

1.2k

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$X\sim \text{Exp}(\lambda)$ use the moment generating function ($m_X(t)$) to find $E(X)$ and $E(X^2)$

Published on 24 Mar 2026 - 13:03

score 106 · Answer 12 · 2026-03-23 22:01:56

106

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Compute $m_Z (t)$. Verify that $m'_Z (0)$ = $E(Z)$ and $m''_Z(0) = E(Z^2)$

Published on 23 Mar 2026 - 22:01

score 47 · Answer 13 · 2026-03-24 13:10:18

47

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How to prove that $\mathbb E(x^n)-\mathbb E(x)^n \ge 0; \quad n \in \mathbb Z_+.$

Published on 24 Mar 2026 - 13:10

score 1.6k · Answer 14 · 2026-03-24 15:26:14

1.6k

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Finding the moment generating function with a probability mass function

Published on 24 Mar 2026 - 15:26

score 1.3k · Answer 15 · 2026-03-23 17:32:23

1.3k

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MGF for Binomial Distribution

Published on 23 Mar 2026 - 17:32

List Question

Showing if $\frac{X}{c}\sim\text{Gamma}(a,b)$ then $X\sim\text{Gamma}(a,cb)$

PDF for Moment Generating Function $(1 +\beta t)^{-\alpha}$ when $\beta > 0$

Simplify and compute the MGF of $[1-(1-(1-e^{-ax})^{N_1})(1-(1-e^{-ax})^{N_2})]^{M-1} $

How to simplify $\sum _{l=1} ^{k} \sum_{j_1 \ge 1} \cdots \sum_{j_l \ge 1, j_1 + \cdots + j_l=k} \binom{k}{j_1 \cdots j_l} \binom{-2}{l} 2^l$

Existence of the MGF of $X_2$

Moment Generating function with Poisson and Exponential distributed variables

Linear combination of power law distributions

The moments of the sum of variables following standard normal distribution divided by the sum of the squares of them

Finding a Joint Moment Generating Function

Find the first moment of a probability distribution governed by a nonlinear first order ODE

$X\sim \text{Exp}(\lambda)$ use the moment generating function ($m_X(t)$) to find $E(X)$ and $E(X^2)$

Compute $m_Z (t)$. Verify that $m'_Z (0)$ = $E(Z)$ and $m''_Z(0) = E(Z^2)$

How to prove that $\mathbb E(x^n)-\mathbb E(x)^n \ge 0; \quad n \in \mathbb Z_+.$

Finding the moment generating function with a probability mass function

MGF for Binomial Distribution

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