# Tagged Questions

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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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### covariance of RVs under a nonlinear transformation

I have a multivariately distributed random 3-vector ...
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### Working with an arbitrary number of sample moments

The $n^{th}$ moment of a distribution can be estimated from a vector of samples $(x_1,x_2,...x_k)$ by: $$\sum_{i=1}^{k} x_i^n$$ Now, let's say I've calculated the first $m$ moments for my ...
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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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### Error in normal approximation to a uniform sum distribution

One naive method for approximating a normal distribution is to add together perhaps $100$ IID random variables uniformly distributed on $[0,1]$, then recenter and rescale, relying on the Central Limit ...
Let $X_i$ be independent, normally distributed random variables, for $1\leq i\leq N$. What is the distribution of $Y_m=\frac1 N \sum_{i=1}^N X_i^m$? Every high school student knows part of the ...