List questions from moment-generating-functions

Published on 22 Nov 2019 - 23:16

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$X_n = \text{Bin}(n,\frac{\lambda}{n})$ for $\lambda > 0$. Show $M_{X_n}(t)$ converges to the MGF of Poisson($\lambda)$ as $n\rightarrow \infty$

Published on 26 Nov 2019 - 21:33

37

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moment generating function , for iid

Published on 01 Dec 2019 - 17:00

114

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Independent binomial distribution

Published on 02 Dec 2019 - 1:33

27

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distirbution of Y random variable

Published on 02 Dec 2019 - 16:15

393

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Let $X$ be a geometric random variable with parameter $\theta$ find $m_X(t)$

Published on 03 Dec 2019 - 0:58

2.7k

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Find pdf of $Z^2$ if $Z\sim N(0,1)$

Published on 03 Dec 2019 - 4:00

336

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Let $m_X(t)$ be the moment generating function of random variable $X$. Prove $m_X(t)=\sum_{k=0}^\infty E(X^k)\frac{t^k}{k!}$

Published on 03 Dec 2019 - 5:39

106

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Let $X\sim\mathrm{Normal}(1,4)$. If $Y=0.5^X$, find $\Bbb E[Y^2]$.

Published on 03 Dec 2019 - 6:11

177

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Linear regression: Distribution of sum of squares from moment generating function

Published on 03 Dec 2019 - 18:08

293

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Determining the distribution and showing it's a pivot

Published on 05 Dec 2019 - 20:37

981

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Finding moment generating function of $f(x) = |x|$

Published on 08 Dec 2019 - 19:17

69

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MGF of an $n$-fold product of independent Rademacher

Published on 09 Dec 2019 - 0:10

299

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What does t represent in the moment generating function?

Published on 09 Dec 2019 - 1:57

696

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Using the moment generating function of uniform random variables to calculate the moments of the uniform distribution.

Published on 09 Dec 2019 - 3:35

List Question

moment generating function find distribution

$X_n = \text{Bin}(n,\frac{\lambda}{n})$ for $\lambda > 0$. Show $M_{X_n}(t)$ converges to the MGF of Poisson($\lambda)$ as $n\rightarrow \infty$

moment generating function , for iid

Independent binomial distribution

distirbution of Y random variable

Let $X$ be a geometric random variable with parameter $\theta$ find $m_X(t)$

Find pdf of $Z^2$ if $Z\sim N(0,1)$

Let $m_X(t)$ be the moment generating function of random variable $X$. Prove $m_X(t)=\sum_{k=0}^\infty E(X^k)\frac{t^k}{k!}$

Let $X\sim\mathrm{Normal}(1,4)$. If $Y=0.5^X$, find $\Bbb E[Y^2]$.

Linear regression: Distribution of sum of squares from moment generating function

Determining the distribution and showing it's a pivot

Finding moment generating function of $f(x) = |x|$

MGF of an $n$-fold product of independent Rademacher

What does t represent in the moment generating function?

Using the moment generating function of uniform random variables to calculate the moments of the uniform distribution.

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