# Questions tagged [covariance]

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

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### Decorrelating variables using Cholesky decomposition

I am looking for a method to decorrelate several variables, so that their covariance matrix is diagonal, while keeping the original mean for each of them. I found this old article which seemed pretty ...
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### Generating from $N_p(\mu,\Sigma)$ and Cholesky decomposition

I know how to generate random observation from $N_p(0,I)$ (applying Box-Muller transformation). But I was wondering how to simulate from $N_p(\mu,\Sigma)$(assuming $\Sigma$ to be pd). I started using ...
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### Covariance and Variance

Given two random variables $X$ and $Y$ , I wish to find $Cov(X + Y, X − Y )$ assuming that $(a)$ $X$ and $Y$ are independent and $(b)$ $X$ and $Y$ are dependent & $Var(X) = Var(Y )$ I started ...
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### Law of large numbers with correlated variables

My sample is a series of measurements of the variable $x$. Measurement t, $x_{t}$, is correlated with $x_{t-n}$. However, as n tends to infinite the correlation tends to zero. If the sample grows, ...
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### Expected Value and variance of a max randomized stocks

Hey guys I have been working on a probability and expected value/variance problem and the problem is: Each day the price of a stock in the market is a random number between 0 and 1 independently of ...
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### Covariance of errors $\text{cov}(\hat{e_{ij}},\hat{e_{i\ell}})$ in Two-Way Anova model

Exercise : Consider the Two-Way Anova model $Y_{ij} = \mu + a_i + b_j + e_{ij}$ with $i = 1, \dots, p$ and $j=1,\dots,q$. Show that : \text{cov}(\hat{e_{ij}},\hat{e_{i\ell}}) = -\sigma^2\left(\...
Let $(X_1, X_2, X_3)\sim N(\mu,\Sigma)$ be a three-dimensional random variable where each coordinates are dependent (i.e. $\Sigma$ has non-zero values outside of its diagonal) I want to know how to ...
Let $X_1,\ldots,X_n,\; n\ge1$ — independent random variables $U(0,1),$ $S_n=\sum_{i=1}^n X_i,$ $Z_n=\max(X_1,\ldots,X_n).$ Calculate $\mathrm{cov}(S_n,Z_n).$ Solution: \$\mathrm{cov}(S_n,Z_n)=\...