# Questions tagged [covariance]

Questions about covariance, a measure of (linear) association between two random variables.

1,138 questions
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### Singular correlation matrix implies linear dependence

Given a random vector $X = \begin{bmatrix} X_1 \\ \vdots \\ X_n\end{bmatrix}$ Suppose that $R = \mathbb{E}[XX^T]$ is the correlation matrix of the random vector $X$ We claim that if $R$ is ...
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### Finite Moments of complicated Stochastic Differential Equation

Suppose I have a SDE of the form: $$dx_i = x_i\left(b_i-\sum_{j=1}^n a_{ij}x_j\right) \,dt + \sigma_i x_i \, d\eta(t)$$ where $\eta$ solves the Ornstein-Uhlenbeck process: d\eta(t) = \lambda \eta(...
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### sampling from a multivariate guassian: intuition behind using cholesky decomposition

I'm trying to understand how sampling from a multivariate gaussian works and why the cholesky decomposition is a way to do it. Let's say we have a 25 dimensional multivariate with a 25x25 covariance ...
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### How does 2D kriging interpolation work?

I have a grid of points Example ...