# Questions tagged [random-vector]

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### Are moduli of components of Fourier transformed Gaussian random vector still independent?

Suppose $X=[X_1,\ldots, X_n]^T$ is a random (column) vector such that: $X_i \stackrel{i.i.d}{\sim} \mathcal{N}(0,\sigma^2), \ 1 \le i \le n$ $\mathcal{F} \in \mathbb{C}^{n \times n}$ is the discrete ...
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### Representation of two Gaussian vectors as sums of independent Gaussian vectors

I know that if we have 1-dimensional Gaussian r.v. X and Y we can find coefficients $a,b$ so that $$X=aY+bZ+E[X-Y]$$ where $Y , Z$ are independent and $Z$ is standard Gaussian. Can we do something ...
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### Multivariate Log-Normal variables with given covariance

Given a symmetric positive definite matrix $\bf \Sigma \in \mathbb{R}^{n \times n}$, I want to find a matrix ${\bf \Gamma} \in \mathbb{R}^{n \times n}$ and a vector ${\bf m} \in \mathbb{R}^n$ such ...
I am reading about convergence of random variables from Wikipedia and I come across this. Note that the condition that $Y_n$ converges to a constant is important, if it were to converge to a random ...