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

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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 ...
2
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0answers
33 views

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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0answers
12 views

Formula of phase correlation

If I have two 2D signals, and one is the shift of another. I can propose such schema for define offset via continious Fourier Transform: $$f_2(x,y)=f_1(x-x_0,y-y_0)$$ Then $$Ff_2(s_1,s_2)=e^{-2\pi ...
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1answer
17 views

Pearson product-moment correlation coefficient of a coin toss

A fair coin is tossed 3 times. Let $X$ be a random variable representing the number of $H$'s appeared in the first 2 tosses, $Y$ the number of $H$'s appeared in the last 2 tosses, and $Z$ the number ...
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1answer
28 views

Generating normal random variables with mean and variance [on hold]

I wish to generate normals $X$, $Y$, and $Z$ with the correlation matrix $R$ but with means $0$, $1$, and $2$, as well as variances $4$, $16$, and $25$, respectively. How would you do this?
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0answers
23 views

Generaling dependent random variables

You wish to generate three standard normals $X, Y$ and $Z$ with correlation matrix given by $$R =\begin{pmatrix} 1.0 & 0.2 & 0.2 \\ 0.2 & 1.0 & 0.2 \\ 0.2 & 0.2 & 1.0 ...
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4answers
5k views

Correlation Coefficient and Determination Coefficient

I'm really new to linear regression and am trying to teach myself. In my textbook there's a problem that asks why $R^{2}$ in the regression of $Y$ on $X =$ the sample correlation between X and Y the ...
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2answers
25 views

Uncorrelated but not independent uniform distribution

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 ...
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0answers
9 views

Normalize and Average weighted

Everyday I receive a data of three variables (neutral, negative and positive). ...
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1answer
25 views

Coefficient of correlation between linearly related random variables [on hold]

A random variable $X = -3Y+10$, where $Y$ is also a random variable and has zero mean. Are they correlated? What is the correlation coefficient in this case? I know that it equal ...
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1answer
726 views

Pearson correlation and metric properties

Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors). Then Pearson's r reduces to Covariance: $$\rho(X,Y) := ...
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2answers
30 views

Correlation Coefficient of Random Variables

Question: My work for parts a and b: Now I'm stuck with part c and don't know where to go or how to get the answer from parts a and b. any help?
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1answer
1k views

Autocorrelation and spectral density in MATLAB

This question is twofold. We have an LTI system that is a first degree Butterworth LP filter with the power TF where fu = 110Hz and ...
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0answers
4 views

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 ...
0
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0answers
22 views

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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0answers
62 views

Correlation function of an asymptotically stationary AR process

I have a great confusion with the autocorrelation function of an AR process. Its derivation usually follows in this way (Haykin, 2007): The difference equation for an AR(M) process, $u(n)$, is ...
0
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0answers
15 views

Simple and partial correlation

(i) The partial correlation coefficient $r_{12.3}=r_{12}-r_{13}r_{23}/(\sqrt{(1-r_{13}^2)(1-r_{23}^2)}$ and the simple correlation coefficient ...
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0answers
14 views

An example where pearson is wildy different to spearman? [duplicate]

Im looking to spearman and pearson, and from what i understand spearman is better at looking at curves. Can i see an example of a small set of data (10 or less) where this difference is large.
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0answers
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Bivariate normal distribution (check)

I need to determine probability. Random variable X has a bivariate normal distribution with mean vector μ and covariance matrix Σ. $$X = {x_1 \choose x_2}, \mu = {-2 \choose 7}, \Sigma = ...
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0answers
14 views

An example of when pearson or regression analysis is drastically different to spearman?

Im looking into spearmans rank. I know pearson and regression struggles with curves, but does anyone have any example of when pearson or regression differs with spearman and what this means? Ideally ...
0
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1answer
26 views

What is the difference in how $\mathrm{R}^2$ and $\mathrm{R}$ values are interpreted?

In statistics, there is the $\mathrm{R}$ value for the product moment correlation coefficient and the $\mathrm{R}^2$ value for the coefficient of determination. In both cases they are described as a ...
0
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1answer
412 views

Relation between Correlation and Convolution

We have two functions of time $f(t)$ and $g(t)$, for which convolution and correlation are defined as following: Convolution: $(f(t)\ast g(t))(\tau) = \int_{-\infty}^\infty{f(t)g(\tau-t)dt}$ ...
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0answers
5 views

Correlation Coefficient in Latent Dirichlet Allocation

Can I use Correlation Coefficient to describe the relationship between two words in LDA? I know JS and KL divergence can give me the similarity between two words but can the similarity given from the ...
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1answer
23 views

Finding correlation Using only Expected values and Variance

I am doing an assignment and arrived at a question that I could not figure out and was hoping for some hints. Let X and Y be two random variables with common variance $a^2$ (a > 0). Suppose that $E ...
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1answer
853 views

Probability of three events occurring given correlation?

I am facing a problem that I cannot find the answer to. I have three variables, A, B and C. There are only two possibilities for each of these, A either happens or it does not, B happens or it does ...
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0answers
19 views

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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2answers
16 views

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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3answers
33 views

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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0answers
20 views

How to find most correlated items?

[Complete noob here, apologies in advance] I have a table which contains a value for each other element in the table. I want to find out what the clusters are of related values (for instance, of ...
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0answers
27 views

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 ...
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1answer
29 views

Correlation and Linear Regression

I'm tasked with this question but unable to proceed on. Q: Calculate the linear product moment correlation coefficient between x and m for these samples: $$ \Sigma x=205,\\ \Sigma m=1240, \\ \Sigma ...
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0answers
20 views

Coupling Brownian Motions

I want to simulate three freight rate indices which are naturally correlated. The freight rate dynamics ($X$) can be modeled as a geometric Brownian motion: $dX_{t} = \mu X_{t}dt + \sigma ...
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1answer
23 views

(a) Calculate the correlation between X and Y, Corr(X,Y).

Suppose X and Y are random variables, such that $$E(X)=5, E(Y)=3, E(X^2)=26, E(Y^2)=13, E(XY)=10$$ We used the equation enter image description here and got $$r=\frac{10n ...
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0answers
21 views

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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1answer
20 views

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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1answer
34 views

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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0answers
19 views

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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0answers
44 views

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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0answers
23 views

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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1answer
16 views

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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0answers
13 views

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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0answers
10 views

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 ...
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1answer
19 views

Variance, Covariance, and Correlation answer check

Two random variables, $Y$ and $Z$: $Y = 0.5+0.6X$ $Z = 0.2+0.3X$ where $X$ is another random variable. You can treat the variance $var(X)$ as a given constant. It may help to give $var(X)$ a name, ...
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0answers
20 views

Covariance matrix of random vector of vectors

I am a beginner in statistics and tried to research my question online without much success. Motivation: I am working on an undergraduate project in cosmology. My problem involves several ...
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2answers
28 views

How can I determine the best relationship for 3 variables, given several data points?

What is the best way to determine the relationship for three apparently related variables? The relationship does not appear to be linear, and may follow a combination of non-linear functions. I have ...
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1answer
58 views

Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
0
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1answer
47 views

Correlation in a series of 1s and 0s [duplicate]

I have a series (in reality I have several series) of 1s and 0s (success and failures) and an "estimated" success-probability as well as the actual success-rate (I can count the 1s in my set). I want ...
3
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5answers
70 views

Suppose $X, Y$ are random variables with the equal variance. Show that $X-Y$ and $X+Y$ are uncorrelated.

Suppose that $X$ and $Y$ are random variables with the equal variance. Show that $X-Y$ and $X+Y$ are uncorrelated. I get I should use the equation $$E[XY] = E[X]E[Y]$$ For the first part I get ...
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0answers
29 views

Correlation in Bernoulli trial

I have a large dataset of tennis-points (who served and if they won etc). Now I would like to check if the points have any correlation with each other (does winning/losing the previous point affect ...
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1answer
28 views

cov(X,XY)? if X,Y is not independent

For two normal random variables , $X$ and $Y$ whose mean are not zero, If $ cov(X,Y) $ is given as $\sigma_{XY}^2 $ , are there any simple way to calculate $ cov(X,XY) ?$