Tagged Questions

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

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Calculating person product moment correlation coefficient on a 3 X 3 table

Usually we are given problems that only involve 2 rows (x and y), but recently saw a problem asking how to compute the correlation coefficient on a table of data that has 3 rows and am not sure how to ...
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Cross-correlation, Fourier transform and Laplace transform: measure of how much signal are alike?

I'm studying electrical engineering and use correlation, Fourier transform and Laplace transform a lot. I know how and when to use them, however, the interpretation I've seen in the lectures still ...
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Generate Correlated Normals

I want to generate normals $X,Y,Z$ with the correlation matrix $R$ but with means $0, 1, 2$ and variances $4, 16, 25$ respectively. How can I do this? Is it possible to apply Cholesky?
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Is this altered formula for correlation still bounded by $-1$ and $1$?

Recall that $$‐1 \le \text{corr}(X,Y) = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \le 1$$ The proof for this bound uses the Cauchy Schwarz inequality, and I've been trying to wrap my head around ...
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Is it true that $\frac{E[(|X - E[X]|)(|Y - E[Y]|)]}{\sigma_X \sigma_Y} = 1$?

Consider the well-known fact that correlation is bounded between $-1$ and $1$: $$-1 \le \text{corr}(X,Y) = \frac{E[(X - E[X])(Y - E[Y])]}{\sigma_X \sigma_Y} \le 1.$$ I've been trying to wrap my ...
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Reducing sequential correlations in Metropolis Algorithm

In our last lab, we use MCMC method to simulate a walker walking in the phase space. Using the Metropolis method, a walker at its currect position will sample another point inside a cube (centered at ...
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Autocorrelation of heaviside functions

I'm trying to find the expression that describes the auto-correlation $r_{xx}(\tau)$ of two heaviside functions $u(t)$. I was told that the result must be $1/2$, which makes total sense, as the power ...
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Spearmans Rank, why does it work?

Looking at spearmans rank, can someone explain how the forumula works, is their anything intuative about it?
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What is the difference between Gaussian White noise and $iid$ noise and how can I check?

If I understand correctly, a series {$X_t$} is $iid$ noise if there is no trend or seasonal component and the observations {$x_t$} are independent and identically distributed with zero mean, while a ...
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Why does Correlation Coefficient concern about the mean of the vector?

$$r = \frac {\sum_{i=1}^n (X_i-\bar X)(Y_i-\bar Y)}{\sqrt{\sum_{i=1}^n(Xi-\bar X)^2} \sqrt{\sum_{i=1}^n(Y_i-\bar Y)^2}}$$ This is exactly the $\cos$ of degree of the angle between vector $X-\bar X$...
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Which variables to use in regression

If I have variables x1,x2,x3,and x4 that have correlation coefficients $-0.9, -0.5, 0.5,$ and $0.9$ to another variable y, what is the effect of choosing different combinations of them in a ...
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Cross correlation of (gaussian distributed) singals with the mean signal gives log-normal density function

The following is my question: I have signals that contains noise, they are of the following form see Figure 1. Then I take the mean signal of all these signals (identical in length and shape). Just ...
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Calculation of a Autocorrelation function and Power spectral density

A sample of a random process is given as: $$x(t) = Acos(2\pi f_0t) + Bw(t)$$ where w(t) is a white noise process with 0 mean and a power spectral density of N0/2, and f, A and B are constants. ...
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Evaluating the spectral density of generated noise through the autocovariance

Arguably more of a question for the signal processing page, but I feel it could also belong here. I'm working on generating noise signals $X(t)$ (with $t \in \left[0,T\right]$ with step size $\delta t$...
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Assess two matrixes overlapping

I have two binary matrixes, of the same size (e.j. 5000x5000). Those matrixes represent the same area, divided in cells of the same size. Each cell of one matrix can be true or false, meaning some ...
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Calculating the coefficient of concordance for vague data

I'm trying to adapt a formula that calculates the coefficient of concordance for vague data. The paper that describes it is here https://www.researchgate.net/publication/...
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Necessary sufficient condition for correlation between last 2 out of 3 normal random variables.

Consider $X,Y,Z$ all standard normal random variables. Now I also want to have some correlation between them. Lets denote these $\rho_{XY},\rho_{YZ}$ and $\rho_{XZ}$. Surely I cannot choose them ...
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Here is an interview question I had and cannot figure out how to solve it. Any hint? Let $X$, $Y$, $Z$ be 3 random variables such that $\mathsf{Corr}(X, Y)=0.9$ and $\mathsf{Corr}(Y, Z)=0.8$. What ...
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What do the eigenvalues of a correlation matrix represent?

I was wondering if there was any special meaning to the eigenvalues/eigenvectors of a correlation matrix. I get what they mean in a covariance matrix, and how that relates to PCA, though. Can you do ...
When reading an old paper from 1921* I find formulas like: $\rho + \frac{\rho(1- \rho^2)}{2\overline{n - 1}} \big( 1+ \frac{9 - 14\rho^2}{6\overline{n-1}} \big)$ which is said to be the median of ...
Correlation between $X\cdot W$ and $Z$ ($Z$ and $W$ are independent)
I have quite a tricky question about correlation. Suppose that there are three random variables $X$, $W$ and $Z$. $X$ and $W$ are correlated and $X$ and $Z$ are also correlated. But, $W$ and $Z$ are ...