# Tagged Questions

Moments are summaries of random variables' characteristics (e.g., location, scale).

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### Existence of the moment generating function and variance

Can a distribution with finite mean and infinite variance have a moment generating function? What about a distribution with finite mean and finite variance but infinite higher moments?
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### Proof that if higher moment exists then lower moment also exists

The $r$-th moment of a random variable $X$ is finite if $$\mathbb E(|X^r|)< \infty$$ I am trying to show that for any positive integer $s<r$, then the $s$-th moment $\mathbb E[|X^s|]$ is ...
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### Combining two covariance matrices

I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two? Linearly interpolating between the two ...
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### Central moments of a gaussian mixture density?

Given the pdf $f(x) = \sum_i \omega_i \mathcal{N}(x; \mu_i, C_i )$ of a gaussian mixture density, where the $i$-th component has mean $\mu_i$ and covariance matrix $C_i$ and the weights $\omega_i$ sum ...
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### Moment generating function of the inner product of two gaussian random vectors

Can anybody please suggest how I can compute the moment generating function of the inner product of two gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each ...
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### How can I calculate central moments of a joint pdf?

Let's say I have two signals $x_1$ and $x_2$, each having $N$ samples, i.e.: $$x_1 = \{ x_{11}, x_{12}, ..., x_{1N} \}$$ $$x_2 = \{ x_{21}, x_{22}, ..., x_{2N} \}$$ The signals are both ...
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### What's so 'moment' about 'moments' of a probability distribution?

I KNOW what moments are and how to calculate them and how to use the moment generating function for getting higher order moments. Yes, I know the math. Now that I need to get my statistics knowledge ...
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### A transform to change skew without affecting kurtosis?

I am curious if there is a transform which alters the skew of a random variable without affecting the kurtosis. This would be analogous to how an affine transform of a RV affects the mean and ...
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