# Questions tagged [correlation]

For questions about correlation of two random variables. Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. Use it with [tag: random-variables] and [tag: probability].

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### Implied Correlation from Gaussian Copula

I am building a spreadsheet model that allows marginal distributions to be correlated together using a Gaussian copula (with prescribed correlation matrix). The inputs into the model are the ...
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### Confusion with Complex Gaussian process with Auto-covariance

I have a complex sequence $z(t)$ in time which I know to be a Gaussian process. I read that the complex Gaussian process is not only characterized by the covariance, but also the pseudo-covariance ...
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### Compute channel frequency resopnse of a channel with fixed bandwidth using Python [closed]

I want to make a visualization of how a channel with a fixed bandwidth (40MHz, 160MHz) changes a channel impulse response. My very simple channel impulse response consists of 3 dirac impulses and is ...
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### Maximize $\frac{\sum x_i r_i}{|x_i|}$

Given a vector $r$, Maximize $\frac{\sum x_i r_i}{|x_i|}$ My intuition is that the solution is when $x_i = k r_i$ for a constant $k$. But I cannot prove it. I have been trying to rearrange it to form ...
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### Can the Wiener-Khinchin theorem be correctly applied to a periodic sound signal (such as a sine wave)?

The theorem speaks about a wide-sense stationary random process. Is, for example, a sine wave with a period 1/400 s considered a WSS (or, in general, a periodic sound signal with multiple frequency ...
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### Expected value, dispersion and correlation coefficient of losses during the day

Every day a kid puts $7$ £1 coins and $9$ £2 coins in his pocket. Each day, in the morning he loses $3$ coins and in the evening of the same day he loses $5$ coins. Find his morning and evening losses'...
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### Fourier transform of a (correlation) function with absolute value in the exponent

I have the following correlation function in time domain defined as $$\left<\xi(t)\xi(s)\right> = \frac{D}{\tau}e^{-|t-s|/\tau}$$ I wish to take the fourier transform of the correlation ...
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### correlation of the sums of samples

Given variables $X$ and $Y$ are positively correlated, if $n$ samples are randomly selected from $X$ and $Y$, respectively, and summed to obtain new variables $X_1$ and $Y_1$, are $X_1$ and $Y_1$ ...
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Given that random variables $X$ and $Y$ are positively correlated, and random variables $Z$ and $W$ are also positively correlated, can it be concluded that $X+Z$ is positively correlated with $Y+W$? ...
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### Omitted Variable Bias

I have a question regarding the omitted variable bias. Its properties of it: the omitted variable is a determinant of the dependent variable,$y$ $X$ is correlated with the omitted variable. I ...
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### Is there true randomness?

In a paper titled "Quantum Randomness: From Practice to Theory and Back", Cristian S. Calude concludes that there is no true randomness in numbers: "The “magic” of the quantum ...
I know how to prove that Spearman's $\rho / r_s$ can be written as $r_s = 1-\frac{6\sum\limits_{i=1}^nd_i^2}{n(n^2-1)}$ with $d_i=R(x_i)-R(y_i)$ when there are no ties. Now I came across the formula ...