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

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57 views

A vector with fixed correlation with existing vector, is it always possible?

Suppose we have a known vector $X$ in $R^n$, and for any vector $Y$ in $R^n$, we impose on it the restriction that it must have a fixed correlation coefficient $r$ with $X$: \begin{align*} ...
0
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3answers
245 views

Prove dot product will get maximum

If we have two identical sets $A_1 = A_2 $, and we were asked to get the maximum sum of multiplying one distinct element from $A_1$ by another distinct element of $A_2$, for all elements in $A_1$. ...
0
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2answers
90 views

Correlation coefficient calculation

Why do we remove of the mean of the data while calculating the correlation coefficient value of bivariate data in statistics? DotProduct/ProductOfLengthOfVectors should always give anyway a ...
1
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1answer
52 views

We have an urn with $5$ blue balls and $15$ red balls.

We remove $7$ without replacement. Let $R$ be the number of red balls removed and $B$ the number of blue balls removed. Do you expect $R$ and $B$ to be positively correlated, negatively correlated, or ...
0
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0answers
15 views

DFT of subdomain of periodic domain

$f(t_i,x_j)$ is a solution of stochastic differential equation on grid. $j=[0,N+1]$, $i=[0,\infty]$ and boundary conditions are periodic: $f(t_i,x_0) = f(t_i,x_N)$ and $f(t_i,x_{N+1}) = f(t_i,x_1)$ ...
0
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0answers
14 views

Multiple variable correlation

I have three data variables (let's call them $A$,$B$, and $C$) that each consist of $14$ samples. What I know is that the combination of $A$ and $B$ is related to $C$. I don't know what kind of ...
2
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1answer
68 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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1answer
38 views

does uncorrelation extend to product of complex random variables?

Give two uncorrelated complex variables, $X$ and $Y$. Are $XX^{*}$ and $YY^{*}$ also uncorrelated, where $*$ means complex conjugation?
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1answer
758 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 ...
0
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0answers
3 views

combining correlation from two different time periods

Suppose I have two time-series $X_t$ and $Y_t$ and I measure their correlations over two different time-periods $\rho_1 = corr(X_i, Y_i)$ for $i \in (t_{1a}, t_{1b})$ $\rho_2 = corr(X_i, Y_i)$ for ...
0
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2answers
42 views

Finding Linear independent vectors

Thanks for clarifications. Now i am posting the question in a different way. Suppose a vector $V$ is orthogonal to vectors $X1$ and $X2$. $X1$ and $X2$ are linearly independent. Now if $V$ is also ...
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0answers
13 views

Check for possible correlations between two stochastic processes [migrated]

So if I have two one-dimensional stochastic processes that are supposed to be correlated, how can I check for their correlation? Ideally in R, thanks!
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1answer
564 views

Correlation between complex random variables

I am struggling to find the correlation between two complex r.vs; X and 1/Y i.e. E{X*/Y}, where '*' denotes the conjugation operator. The complex r.s X and Y are correlated with each other with known ...
0
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1answer
9 views

In a simple regression model estimated using OLS, the covariance between the estimated errors and regressors is zero by construction

Is this statement true or false? I seem to remember that this relationship does not hold when the regression has no intercept, however my teacher said that this was true regardless of whether we ...
11
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2answers
13k views

Generating correlated random numbers: Why does Cholesky decomposition work?

Let's say I want to generate correlated random variables. I understand that I can use Cholesky decomposition of the correlation matrix to obtain the correlated values. If $C$ is the correlation ...
1
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1answer
6 views

How represent correlation of $(f_i - f_j) $ and some $ y$ by $cov(f_i, f_j)$, $cov(f_i, y)$ and $cov(f_j, y)$?

I am reading this paper: Face Alignment by Explicit Shape Regression. One of the significant step of algorithm which proposed in these paper connected with correlation. But my knowledge about ...
2
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2answers
57 views

Generating correlated random variables with discrete distribution

I would like to find a simple way to generate two correlated random variables under the condition that each r.v has a same discrete distribution (for example Bernoulli distribution) This link provides ...
0
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1answer
39 views

Correlation coefficients of X and Y [closed]

I was wandering if anybody could help me with the following question. I am fairly new to correlation coefficients and was attempting to tackle this question but was unsure how to do so? Thanks.
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0answers
9 views

Autocorrelation of a random sequence is given below. A way to shuffle to decorrelate?

3.0000 1.7071 - 1.7071i 0 - 1.0000i 0.2929 + 0.2929i 1.0000 0.2929 - 0.2929i 0 + 1.0000i 1.7071 + 1.7071i The ...
0
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2answers
26 views

Calculating the correlation coefficient between least square estimates

PROBLEM STATEMENT: Consider the following 2-variable linear regression where the error $e_i$ 's are independently and identically distributed with mean $0$ and variance $1$; $$y_i = α + β(x_i − \bar ...
0
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1answer
32 views

Cross-correlation of identical sets: not getting expected result

I'm trying to work out the correlation coefficient of two sets using a given formula, but I'm not getting a perfect correlation when using identical sets. The correlation between a client’s ...
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0answers
22 views

Transpose is just the way of generalizing a dot product?

It seems like $a^Tb$ is the same as writing $a \cdot b$ in matrix form. 1) Why is $n \times 1$ and $n \times 1$ matrix multiplication undefined? 2) Is this just a generalization of the dot ...
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2answers
11k views

Calculating the variance of the ratio of random variables

I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is $$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$ but, how do I derive it from "common" ...
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0answers
12 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]E[Y] $$ ...
1
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1answer
21 views

Question about uncorrelatedness of random variables and distributions

I was wondering, if two random variables are dependent, does that mean that they must be correlated? does one imply on the other or vice versa? Also, if I know that a joint distribution of two ...
0
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0answers
35 views

Generalizing Pearson's coefficient to determine properties of embedded manifold

I have the following dilemma: We know that for random vectors we have Pearson's coefficient of skewness. I think you all agree that in some sense it measures the shape properties of the ...
0
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1answer
44 views

How can I remove correlated noise spikes from 2 signals?

I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I ...
0
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1answer
23 views

correlation matrix of an AR(1) process

Suppose we have a process whose elements follow an AR(1) pattern with correlation $\rho$. I am confused, concerning the following: The exact form of the $(i,j)$ element of the correlation matrix P is ...
0
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2answers
27 views

Question on Spearman's Rank Correlation Coefficient

I'm doing some practice questions in my statistics book, and started doing this one: Find Spearman's rank correlation coefficient between X and Y for this set of data: ...
0
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1answer
412 views

What does the multiplication of standard deviation of two variables gives?

If we need to find the correlation between two variables it is given by the formula - co variance of two variables divided by the multiplication of Standard deviation of the two variables. My ...
2
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0answers
38 views

Calculate mean and correlation of a stochastic process

I am given the Stochastic process $Y_n$, where $n \in Z$ defined by: $ Y_n = X_n - X_{n-1}$ where $X_n$ is a process with independent and identically distributed geometric variables $X_n \sim G(p)$ ...
0
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0answers
17 views

Correlation between ordinal variables

I want to know the correlations between 3 groups of variables which are oridinal (rating of 1 to 10). I have followed the formula on wiki and computed the Kendall tau-b correlation coefficients ...
0
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0answers
7 views

What are the bounds on total correlation given partial correlations?

Given two random variables X and Y, each with 3 million outcomes, if we compare the first, second, or third million of these outcomes, we can compute the partial correlations between X and Y. If each ...
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0answers
28 views

Limit of correlation function using transfer-matrix method

This question is about a stochastic process theory. I really very bad in this topic. That's why I have to ask for help. I may mistranslate some terms but I'll do my best to give you right information. ...
1
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1answer
39 views

Why is my phase correlation not equal to the real correlation?

If I understand the correlation theorem correctly, it states: $ f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\}, $ also called a phase correlation. Above ...
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0answers
48 views

Minimize correlation between input and output of a linear system

I am not sure if "minimize correlation" is the right title for this issue but I could not find a better sentence to describe what I would like to achieve. Let's say that I have a black box with ...
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1answer
15 views

Does correlation (PMCC) require variables to be normal

When calculating product moment correlation coefficient between two variables, say height and weight, is it necessary that the variables are normally distributed for the PMCC to be valid/relevant. ...
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1answer
18 views

Statistics for correlations with many (0,0) values

Suppose you have a large but finite collection of tweets. You want to know whether talking about football tends to correlate with talking about basketball. You can generate a table for a few hundred ...
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0answers
12 views

Question about the relationship between correlations

I am trying to figure out the relationship between correlations of variables where one of the variables defined as the difference between two other variables. I have variables x and z, which are ...
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1answer
25 views

Finding peaks and oscillations in a signal

I am working on a problem where I'm analysing a signal and trying to find a measure of whether a roughly Gaussian shape appears or oscillations - though the oscillations may not be periodic. For ...
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1answer
27 views

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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2answers
35 views

Correlation in scatter plot

This may be a very basic matter for statisticians, but I still have no intuition for this sort of thing. Here goes: I have two quantities (the nature of which is irrelevant) which I suspect to be ...
0
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0answers
29 views

explanation : Example of Gaussian random process?

Can any one explain to me how to answer the question and what is the Gaussian random process in a simple way. I know how we find the C xx from R xx the rest of the answer I don't understand why all ...
0
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0answers
22 views

Correlation/Regression for Continuous and Discrete data

I want to correlate a data where one axis is continuous (ranging from 0 to 1), other axis is discrete. Discrete axis scale is 1 to 5 (1 is for Strongly Disagree and 5 is for Strongly agree). How ...
0
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0answers
31 views

Calculation the Correlation Matrix of a Random Observation Vector

I've googled and looked around on StackExchange but I can't quite find the answer. I'm trying to calculate the correlation matrix R. Below I've included a screenshot of some text that explains how. ...
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2answers
132 views

Does $0$ correlation imply independence for marginally normal distributions?

Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$. Can someone give a hint why this is true ?
0
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0answers
22 views

The correlation between alpha and beta

Consider the following 2-variable linear regression where error $e_i$'s are independently and identically distributed with mean 0 and variance 1; $$ y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ...
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0answers
55 views

Sampling a distribution with restrictions: eliminating the correlation between two variables

I have a collection of $400.000+$ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
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0answers
25 views

How to convert principal components of a $2\times2$ covariance matrix into principal components of a correlation matrix

All, I am wondering if there is any way to mathematically express the change in direction of the principal components from the $2\times2$ covariance matrix to the correlation matrix. In other words, ...
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0answers
35 views

Data analysis: How did people beat the Great Hall game?

This is the game: There is a Great Hall with 102 doors. 100 of these doors lead to one of 100 different side rooms. The 101st door, at the end of the Great Hall leads to the Great Tower, where ...