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Ricardo Andrade
Ricardo Andrade
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Variance of euclidean norm of gaussianGaussian vectors

Let $X$ be a gaussianGaussian vector in dimension $n$, with $0$ mean and covariance identity. Let $A$ be a square matrix of size $n$, and $Y = A X$. Let $N$ be the square of $Y$ euclidean norm: $N = \sum Y_i^2$. One computes easily the mean of $N$: $E[N] = \text{Tr}(A A')$. But what about its its variance  ?

Variance of euclidean norm of gaussian vectors

Let $X$ be a gaussian vector in dimension $n$, with $0$ mean and covariance identity. Let $A$ be a square matrix of size $n$, and $Y = A X$. Let $N$ be the square of $Y$ euclidean norm: $N = \sum Y_i^2$. One computes easily the mean of $N$: $E[N] = \text{Tr}(A A')$. But what about its variance  ?

Variance of euclidean norm of Gaussian vectors

Let $X$ be a Gaussian vector in dimension $n$, with $0$ mean and covariance identity. Let $A$ be a square matrix of size $n$, and $Y = A X$. Let $N$ be the square of $Y$ euclidean norm: $N = \sum Y_i^2$. One computes easily the mean of $N$: $E[N] = \text{Tr}(A A')$. But what about its variance?

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msfr
msfr
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Variance of euclidean norm of gaussian vectors

Let $X$ be a gaussian vector in dimension $n$, with $0$ mean and covariance identity. Let $A$ be a square matrix of size $n$, and $Y = A X$. Let $N$ be the square of $Y$ euclidean norm: $N = \sum Y_i^2$. One computes easily the mean of $N$: $E[N] = \text{Tr}(A A')$. But what about its variance ?