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

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21 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
12 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
39 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 ...
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2answers
31 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 ...
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2answers
34 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. ...
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1answer
24 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
37 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
13 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} ...
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2answers
29 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 ...
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1answer
133 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
10 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
15 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
161 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
94 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
11 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
39 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
19 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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66 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
26 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
25 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
52 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 ...
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1answer
50 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
402 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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8 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 ...
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1answer
81 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
20 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 ...
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1answer
42 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( ...
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0answers
64 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) = \#\{ ...
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1answer
147 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 ...
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2answers
68 views

Correlation coefficient

I'm a little puzzled by the whole random variable thing. I've got two random variables, $\mathcal{X}$ and $\mathcal{N}$, both with gaussian distribution with mean = 0 and $\sigma_{\mathcal{X}}^2$ and ...
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1answer
32 views

Estimate correlation coefficient of unknown variable

Consider variable y depends on variable x and z linearly. I have $100$ sample values of $y$ and corresponding $x$ but don't have any values of $z$. The functional model is $$y = \alpha_1x + \alpha_2z ...
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3answers
23 views

Correlation and what it tells me

OK, I need a little help here. I have attached two pictures; Data and Chart in which the data shows a correlation coefficient of 0.283168 which was calculated by Excel. Can someone please tell me ...
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1answer
88 views

Correlation Coefficient Distribution Function: An Apparent Discrepancy?

I'd like to explain an apparent discrepancy between: (1) The sample correlation distribution function between sample vectors for a bivariate, correlated random variable (correlation coefficient = ...
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0answers
75 views

Spatio-temporal triple correlation

I would like to simplify if possible the spatio-temporal triple correlation of the following function: $$f(\vec{x},t)=\delta(\vec{x}-\vec{x}_0(t)) \otimes f_p(\vec{x})$$ where $\delta$ is the Dirac ...
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0answers
20 views

What is correlated with what in a linear regression?

I'm trying to make sure I understand the ins and outs of a linear regression and am making a table for what is correlated with what, so just want to see if I have everything included. I'm looking at ...
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1answer
62 views

How can we derive expectation of two dependent normal distribution?

$\mathbf{X}$ and $\mathbf{Y}$ are each dependent normal random variable, then how can we derive like this one? $$\mathbf{E}\{e^{\mathbf{X}}e^{\mathbf{Y}}\}$$ I know the each first moment is ...
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0answers
54 views

How to interpret autocorrelation of images?

Say we have a multiple grayscale images $I_i$ collected as a matrix $M = [I_1\ I_2\ I_3\ldots I_n]$ What exactly does its autocorrelation $R_{MM} = M M^T /{n}$ tell me? According to Wikipedia ...
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0answers
18 views

Principal Component Regression

Suppose that Z1, Z2 and Z3 are the principal components of a data set and Y is a vector of the response variable. The correlation coecients between Y and Z1, Z2 and Z3 are 0.25, -0.4 and 0.7, ...
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0answers
13 views

Indepedence of sample means of two orthogonal Gaussian vectors?

Suppose $\boldsymbol{x}_{1}$ and $\boldsymbol{x}_{2}$ are Gaussian vectors with each distinct but arbitrary means and covariances, i.e., the elements of each vector are generally intra-correlated. ...
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0answers
68 views

Using mutual information to estimate correlation between a continuous variable and a categorical variable

As for the title, the idea is to use mutual information, here and after MI, to estimate "correlation" (defined as "how much I know about A when I know B") between a continuous variable and a ...
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0answers
24 views

Find solution of correlation matrix equation

Suppose ${X}$~$N(0,\sigma^2\Sigma)$, with $\Sigma$ being unknown correlation matrix. How to find a solution of $\Sigma$, such that for $Z=\alpha'X$, we have $var(Z)=C$. (Suppose C is properly chosen ...
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0answers
21 views

Autocorrelation Clarification

Could anyone help clarify a high level explanation of autocorrelation? I understand that it is a measure of correlation between a timeseries and a lagged version of the same series. If we have take ...
2
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1answer
278 views

Maximum and minimum Correlation Coefficient

I have a question regarding the correlation coefficient. The inspiration is from a story where a student collected a set of $(X,Y)$ pairs, but lost the pairings. Hence, he is left with two sets of ...
2
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2answers
89 views

Given X and Y are correlated and Y and Z are correlated what is the range of correlation between X and Z?

How can I calculate the range of correlation of two variables X and Z given I have the correlations of X and Y, and Y and Z? I've found a few resources around, namely this, but I'd like a research ...
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1answer
44 views

Generating correlated random numbers from Normal Distributions

If I have a sequence taken from X~N (μ1 , σ1 ). Is it possible to generate a sequence of numbers drawn from Y~N (μ2 , σ2) such that X and Y have correlation ρ?
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2answers
1k views

Expected value of two dependent variables is still a product of expectations

For independent variables we have $E[XY]=E[X]E[Y]$. Now, since I could not find a statement that the converse is also true, I suspect that there are examples of dependent variables where this relation ...
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1answer
68 views

Countermonotonicity and minimum linear correlation coefficient

In an example exercise they question whether it is possible to construct a bivariate distribution of $LN(0,1)$- and $LN(0,4)$-distributed random variables, where $LN(\mu,\sigma^2)$ is the log normal ...