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

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2answers
35 views

What is this idea of “Minimum Correlation”?

So I was having a read of this paper here: Minimum correlation for any bivariate Geometric distribution. On the first page of he paper we encounter the following definition of "minimum correlation": ...
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1answer
25 views

Mutual information decrease with coarse-graining

Let $X,A,Y,B,C,D$ be random binary variables. $D$ is independent from $X,A,C$ and $C$ is independent from $Y,B,D$. Is it true that: If $I(Y:B|D=0)\leq \epsilon$ then $I(X\oplus Y:A\oplus ...
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2answers
48 views

Autocorrelation and var-cov matrix

$$Y_t=\beta_1+\beta_2 X_{t2}+\dots +\beta_k X_{tk}+\epsilon_t \qquad (t=1,\dots,T)$$ $$\epsilon_t=\rho \epsilon_{t-1}+v_t, \qquad v_t \sim \mathrm{i.i.d.}(0,\sigma^2_v)$$ GLS estimation under AR(1) ...
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2answers
32 views

Determine range of $\rho$ in correlation matrix

I was asked a question and I was wondering if you can help solve it. Given are $3$ random variables $A$, $B$and $C$ all having the same correlation. So the correlation matrix looks like: ...
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1answer
23 views

Does correlation have to be in the context of (Gaussian) normal distribution?

I am not quite familiar with the concept of correlation. The Pearson's correlation coefficient is defined as: $\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ...
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1answer
45 views

How to calculate the HHG (Heller Heller Gorfine) correlation

HHG (A consistent multivariate test of association based on ranks of distances) is introduced in: Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association ...
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1answer
50 views

Correlation with many zero values

I have data for selling books from 2 bookstores for 100 days. For the first 90 days, no book was sold. Then the following books were sold Day# - BookStore1 - BookStore2 Day1 - 0 - 0 ...
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2answers
50 views

Strong vs weak relationship in this correlation

I produced this plot and regression line in R and I thought my results were quite odd. Is the relationship of the correlation determined by how steep the regression line is? So in this case it isn't ...
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1answer
72 views

Variance from joint random variables?

So I have 20 different 'weeks' that are being considered as part of a weight loss exercise. The weight lost each week is distributed normally around mean $\mu =0.8kg$ and std. deviation $\sigma^2= ...
1
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1answer
267 views

How to explain tie-correction for Spearman's Rank Correlation?

In Mathematics at my college we are being taught correlation in which when there are ties in ranks we take average rank for all of the ties and then total correction factor is added summation of ...
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1answer
105 views

graph in excel to represent correlation of 3 parameters

I have some data in excel and I would like to make a graphical representation of those data. Structure of my data: persons ID : from 1 to 485 to every person, there is one parameter like average ...
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1answer
68 views

Correlation between two random variables

Show that if $\rho_{XY} = +1$ then $X=a+bY$ for some constants $a,b$ and $b>0$. How would I go about showing this? Note: $$ \rho_{XY} = \frac{\mbox{Cov}(X,Y)}{\sqrt{\mbox{Var}(X)\mbox{Var}(Y)}} ...
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1answer
50 views

Correct way to evaluate correlation of a computer model with multiple human annotator scores

I have posted this question to CrossValidated without lack. If anyone from this community can give some insights, I would be really grateful. Assume we have 3 annotators, each one of which has ...
0
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2answers
32 views

Showing $Cor(X,Y) = 1$ if $a>0$ and $-1$ if $a<0$

Suppose X and Y are random variables such that $Y=aX+b$ and $a$ and $b$ are constants. Show that $Cor(X,Y) = \begin{cases} +1 &\mbox{if } a > 0 \\ -1 & \mbox{if } a < 0. \end{cases}$ ...
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1answer
23 views

Comparing ranking algorithms

If I have several different ranking algorithms and a 'correct' ranking, is there a good way of "scoring" the alternative rankings given by the algorithms against the reference one? For example: ...
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1answer
38 views

Linear regression with normalized variables

Suppose I have two variables X and Y such that mean(X) = 0 = mean(Y) and sd(X) = 1 = sd(Y). The slope of the linear regression line for Y vs X is cov(X,Y)/var(X) = corr(X,Y) since X and Y are ...
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0answers
66 views

Autocorrelation Function and Power spectrum from ACF

In my assignment I am required to write or use a C code to find the autocorrelation function of a given function and then find the power spectrum from it. The function is as follows: $$f(t) = \cos(10 ...
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0answers
24 views

correlation estimator

Suppose I have independent variables $X$ and $Y$ which follows exponential distribution with parameter $\lambda$. I want to find the variance of correlation estimator $\hat{\rho}$ which is defined as: ...
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0answers
17 views

stats project - good model, what to do with it?

I've recently been working on a stats project for school. I have been comparing a country's 'quality of life index' with 'moral' opinions survey to see if there are relations. Here's some example ...
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1answer
24 views

correlation between two series

let us consider following two series $$y[t]=a_1\sin(\omega_1 t + \phi_1) + a_2\sin(\omega_2 t + \phi_2)+ \cdots + a_p\sin(\omega_p t+\phi_p) + z_1(t)$$ and $$y_1 [t] = A_1(\sin(\omega_1 t+\phi_1) ...
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0answers
15 views

Maximum correlation of n variables

For $n>2$ variables, one cannot arbitrarily choose the correlations $\rho_{ij}$ because the resultant correlations must obey the law of cosines. Equivalently, the covariance matrix between them ...
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3answers
43 views

Variance of X - Y

If X and Y are random variables with correlation coefficient 0.7, each of which has variance 6, what is the variance of X−Y? Enter your answer as a decimal. Using the information given, I was able ...
1
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2answers
39 views

Covariance of $10$ Coin Flips

I'm getting the hang of using the properties of Covariance to make calculating it much easier but I'm stuck on this one. Fair coin tossed $10$ times. Let $X$ denote number of heads observed and ...
1
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2answers
68 views

Covariance of three dice rolls

I understand this question has been asked but I have a different comment to make on the matter and wondering if someone could help me. Let Z1,Z2,Z3 be values resulting from three tosses. ...
1
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1answer
31 views

Simple linear regression prove variables are uncorrelated:

I am working on the following problem: In a problem of simple linear regression, $$Y = \hat\beta_0 + \hat\beta_1 x(bar),$$ show that the random variables $\hat\beta_1$ and $Y$ are un-correlated (All ...
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1answer
58 views

Fair Coin Covariance

Consider an experiment in which three fair dice are tossed simultaneously and independently. Let $Z_1,Z_2,Z_3$ be the values resulting from the three tosses. Define $X=Z_{21}+Z_{22}−Z_{33}$ and ...
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1answer
24 views

What does the “empirical” autocovariance function represent?

My professor gave me the sequence ${X_n} = {1,5,5,1,5,5,...}$ and asked us to compute the empirical autocovariance function given below. $$\displaystyle \hat \rho(1) = \lim_{N \to \infty} \frac{1}{N} ...
0
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2answers
37 views

Is the autocovariance function of a sequence identically zero if the sequence is iid?

My professor gives the following definition for the autocovariance function. $$\rho(i,j) = Cov(X_i , X_j)$$$\\$If I have a sequence that is iid, when i compute $\rho(n,n+1)$ for $n \geq 0$, I found ...
2
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1answer
445 views

Distribution of the sum of normal random variables

Let $X\sim \mathcal N(\mu_X,\sigma_X^2),\ Y\sim \mathcal N(\mu_Y,\sigma_Y^2)$ two normal random variables and $a,b\in \mathbb R$. If $X,Y$ are independent, then $$aX+bY\sim \mathcal ...
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0answers
13 views

Correlation matrix of time series is same as correlation matrix of its difference

I computed the correlation matrix between the percent change in the price of 6 stocks. Then I differenced the stock percent change data as if it was a time series, and the correlation matrix is almost ...
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0answers
17 views

Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ...
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1answer
218 views

Autocorrelation and spectral density in MATLAB

This question is threefold. 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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1answer
390 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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1answer
16 views

Autocorrelation of a sequence of vectors

Let's say I have a sequence of 2-d vectors and I want to calculate autocorrelation of this sequence of vectors. If $V_i$ where i = 1:n is the list of vectors then acf as a function of time lag 't' is ...
2
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1answer
41 views

$\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$

$\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ is a convex risk measure, but it fails the subadditivity property in order to be called coherent. A mapping ...
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0answers
23 views

Cross correlation computations

What are useful ways/formula for calculating sample cross correlations (i.e. correlation factors between individual components of two different random variables). Say I have two sample matrices, $X$ ...
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0answers
9 views

Finding correct values based on information from two arrays

Consider the following scenario: Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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0answers
119 views

Generate correlated random numbers precisely

Let's assume I want to generate k samples of n random numbers, that are correlated according to a given correlation matrix C (e.g. $n = 3$): ...
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1answer
36 views

Correlation: Concept to Formula

In digital signal processing, we calculate the correlation between two discrete signals by multiplying corresponding samples of the two signals and then adding the products. Where does this ...
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0answers
30 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
2
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1answer
53 views

probability need help on correlation problem [duplicate]

A deck of 52 cards is shuffled you are dealt 13 cards. Let $X$ and $Y$ denote, respectively, the number of aces and the number of spades in your hand. Show that $X$ and $Y$ are uncorrelated. I try to ...
3
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1answer
52 views

finding the unspecified ${\bf E}[X]$ and $\rm var(X)$ given the expectation of higher powers of $X$

Homework Problem: It is known that a for a standard normal random variable $X$, we have ${\bf E}[X^3]=0$, ${\bf E}[X^4]=3$, ${\bf E}[X^5]=0$, ${\bf E}[X^6]=15$. Find the correlation coefficient ...
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4answers
563 views

Inferring covariance cov[X,Z] from cov[X,Y] and cov[Y,Z] of known distributions

Suppose X, Y and Z are real random variables of known distributions. If one knows the covariance $COV(X,Y)$ and $COV(Y,Z)$, is it possible to infer $COV(X,Z)$?
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0answers
9 views

How to order a set of attributes such that their correlation matrix concentrates high correlation terms around the diagonal?

Suppose there are n attributes that are being tested for correlation with one another. We need to find the order in which these attributes must be placed along the rows as well as columns such that ...
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0answers
7 views

Similarity between two matrices/lattices

I'm looking at the evolution of matrix in time where every coefficient can only be +1 or -1, from physical point of view it could be an Ising model on finite lattice. I'm interested in a variable ...
0
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1answer
343 views

How to construct a covariance matrix from a 2x2 data set

so if given a covariance matrix I can find the eigenvalues and move forward from there... but I seem to have trouble with the step before if I am given a data set and am told to create the covariance ...
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0answers
10 views

Correlation 4-point

I need to calculate $\langle x_{i}x_{j}x_{k}x_{l}\rangle $, where $$ \langle f(x) \rangle = \int e^{-\frac{1}{2}A_{ij}x^{i}x^{j} - \frac{\lambda }{4!}\sum_{i}x_{i}^{4}} f(x)d^{n}\mathbf x , $$ for ...
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0answers
23 views

Weighted Pearsons Correlation

I am a software engineer so please bare with me. I am currently calculating the ppmc coefficient of a series of data over unequal time periods. I wish to weight data that was recorded within the last ...
0
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1answer
49 views

How to deal with the following problem of correlated random variables?

I have the following information: $\left[ \begin{array}{l} {X_1}\\ \vdots \\ {X_K} \end{array} \right]$ are correlated random variables with (zero mean, unit variance) covariance matrix $\left( ...
2
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0answers
67 views

Show that a function is log supermodular

I have been struggling with the following Let $X$ be finite and a poset $P = (X, \leq)$, and for any $A \subseteq X$ we can define the function $f_A$ on $\mathcal{P}(A)$ as follows $$ f_A(Y) = \#\{ ...