# Tagged Questions

For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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### Variance of the sum of correlated variables

If the variance of two correlated variables is: $$Var(r_1+r_2)=\sigma^2_1+\sigma^2_2+2\textrm{cov}(r_1,r_2)=\sigma^2_1+\sigma^2_2+2\rho\sigma_1\sigma_2$$ where $r_1$ and $r_2$ are vectors, then what ...
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### Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$

Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$, given that the autocorrelation of $x$ is: $$R_{xx} = \frac 1{n\pi}\sin\left(\frac {\pi}{2}n\right).$$ I've tried to ...
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### Given the correlation matrix, estimate the value of a random variable based on the value of other random variables. [closed]

A process generates $N$ random variables $(X_i \mid 1 \leq i \leq N)$. The process is run $K$ times, and the values of each random variable $X_i$ is observed. Based on this data, the following ...
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### Can I ignore multicolinearity problem if all the regression coefficients are highly significant?

Can I ignore multicolinearity problem if all the regression coefficients are highly significant? My data is large enough and all the resulting coefficients are significant enough in less than 0.01 ...
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### Is a correlation matrix with positive determinant PSD?

Please note: I'm not interested in the difference between positive definiteness and semi-definiteness for this question. A correlation matrix is a symmetric positive semi-definite matrix with 1s down ...
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### statistical test for comparison of time series of rare events

I have two time series of a binary variable which assumes value 1 if an event happens and 0 otherwise. Both series report the occurrence of the same event and are not necessarily equal because the ...
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### Interpretation of correlation (coefficient)

In an discussion we were confronted with a very special opinion about correlation in respect of financial assets. The widely used correlation coefficient is used here to give an idea about how ...
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### First and second moments of two correlated functions

I am trying to find the first and second moments of the following: $k=mk^{-b}$ where $m \sim U[a,b]$ (discrete) and $k^{-b}$ is a power law distribution I know how to find the first and second ...
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### How to generate correlated random numbers with specific distributions?

After read the answers of some similar questions on this site, e.g., Generate Correlated Normal Random Variables Generate correlated random numbers precisely I wonder whether such approaches can ...
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### Normalize and Average weighted

Everyday I receive a data of three variables (neutral, negative and positive). ...
Let $X = (X_1, X_2)$ be uniform distributed on $\{(-1,0), (1,0), (0,-1), (0,1)\}$. First of all I want to show that $X_1$ and $X_2$ are uncorrelated but not independent. Secondly I thought about ...