Questions tagged [covariance]

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

1,138 questions
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centering two variables $X$ and $Z$ makes $cov (X,XZ) = 0$

I've read that centering two normal (or symmetrical) variables $X$ and $Z$ affects correlation of centered $X$ with interaction term $X\cdot Z$ in such way, that this correlation $cor(X-EX, X\cdot Z)$ ...
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Standard Error of Sample Variance

I have a time-series of values $X_1, X_2, \ldots, X_t$, for which I compute sample variance: $$\hat{\sigma}^2 = \operatorname{var}(X_1, \ldots, X_t)$$ (unabiased estimator using $\frac{1}{t-1})$. ...
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Covariance of a mixture of Gaussians

I have seen this question asked, but in a strange way that I do not think is equivalent. If someone can show that the formulations are identical, I would be grateful. Suppose with probability $p$, ...
Let X and Y be two nonnegative, integer-valued random variables. Is there a way to find the joint probability mass function, i.e. $$\mathbb{P}(X= k, Y= h)$$ for some $k,h\geq 0$, given the ...
I have to compute a covariance. But I have some difficulties. My covariance has the following shape :  \sum\limits_{a=1}^t\sum\limits_{b=1}^t\sum\limits_{c=1}^t\sum\limits_{d=1}^t\operatorname{cov}\...