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

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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

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: $dX_{t} = \mu X_{t}dt + \sigma X_{t}dW_{t}$...
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0answers
25 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 scalar-...
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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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2answers
30 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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5answers
80 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 $$E[(...
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1answer
49 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 ...
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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
32 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) ?$
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1answer
41 views

Interpreting the scatter plots of two random variables

Suppose I sample random variables A and B from normal distributions. When I do a scatter plot of these two variables I see a ...
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2answers
33 views

Correlation of sum of independent variables with its parts. if Z=X+Y, what is Cor(Z,X)?

If $Z = X + Y$, where $X$ & $Y$ are independent random variables, is there some formula to work out $\rho(Z,X)$, based on $\sigma_X$, $\sigma_Y$? For example, I've noticed that for $\sigma_X$ = $...
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1answer
39 views

finding correlation coefficient given conditional expectations

Given $Y1$ and $Y2$ have a bivariate normal distribution where $E(Y1|Y2)=4.7-0.16Y2$ and $E(Y2|Y1)=0.8-Y1$ and conditional variance is 3.64. How can I find the correlation. I have tried the $E(E(Y1|...
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0answers
26 views

Are there any errors in my summary of stationarity? and some more questions.

I've posted questions about stationarity, but I cannot get answers satisfying me because of my vague question. Thus, I read more times about definitions about stationarity, summed them up, and brought ...
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0answers
12 views

Correlation coefficient function (function of time) has obvious hape but weak absolute value

I am doing a research about a 2D space. I am looking at the angle alinement between the eigenvalues of stress and strain respect to time. When I plot the angle alinement vs. time, it showed an ...
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1answer
12 views

Correlation coeffcient expressed in a different form

If $X_j = a + bX_i$ and $X_i = a' + b'X_j$ how does one show that the correlation coefficient can be written as: $\rho_{i,j} = b \frac{\sigma_i}{\sigma_j}=b'\frac{\sigma_j}{\sigma_i}$ ?
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0answers
14 views

Pearson correlation of neural responses with it's linear estimation

I am trying to anderstand the following fact: Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r} - \mathbf{f}(s_0)) + s_0$ where $\mathbf{w}$ is a vector of ...
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1answer
29 views

Distinction between correlation coefficient and coefficient of determination

In my stats class, I am learning about correlation coefficient and coefficient of determination. I dont understand what the difference is between them. there are $r,\,$ $r^2$ and $R^2$. $r^2$ and $R^...
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1answer
18 views

Correlation between a random variable and its rank

Let $X_1,\ldots,X_n$ be a random sample from $U(0,1)$ and $X_{(1)}<\ldots<X_{(n)}$ be the corresponding order statistics. Define, $$ R(X_1) = r\quad \text{if}\quad X_{(r)} = X_1;\quad r = 1(1)...
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2answers
39 views

Generate two negatively correlated data in excel

Let's say that we have two prices that are negatively correlated to each other, for instance we have price $p_1$ and we want to generate negatively correlated price $p_2$ with the following ...
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0answers
31 views

Determining whether or not random variables are correlated

I'm working on the following problem: Consider random variables $X$ and $Y$ such that exactly one of them is equal to $0$. The other then takes the value $1$ or $-1$ with equal probability (ex:...
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0answers
8 views

zipf and lognormal with a particular correlation

I have been struggling on how to generate a correlated zipf and lognormal distribution. I want to generate a set of data ,say,$(X,Y)$,where $X$ is the popularity of file described by zipf,$X=1,2,3......
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1answer
20 views

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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0answers
13 views

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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1answer
37 views

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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2answers
66 views

question about correlation of variables

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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0answers
31 views

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 ...
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0answers
35 views

Meaning of horizontal bar in old formula (paranthesis?)

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 ...
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1answer
33 views

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 ...
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1answer
18 views

Why is $Y$ and linear function of $X$ if the correlation equals $+1$ or $-1$?

Just looking for a proof of $\operatorname{Cor}(X,Y) = \begin{cases} +1 & \text{if } a>0, \\ -1 & \text{if } a<0, \end{cases}$ where $X$ and $Y$ are random variables such that $Y=aX+b$ ...
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1answer
27 views

Calculate $P[A,B,C]$ from $P[A,B]$ and $P[B,C]$

I have 3 (not independent) events $A, B, C$ and I know everything about how any two of them correlate. For example, I know: $$ P[A], P[B], P[C], P[A,B], P[A,C], P[B,C], P[A|B], P[A|C], P[B|C], P[B|A],...
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28 views

Implementing Normalized Cross-Correlation using FFT - How to?

Is there any way to calculate the normalized cross correlation between 2 signals by using the FFT? (I managed to implement it already for standard cross correlation equation). Thanks in advance,
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19 views

Modelling Correlation between CAC and DAX index

I am working on the implementation of a Garch-copula model ("Patton" approach who did it on exchange rate) to model the correlation between these two index. It is implemented now. Basically, you first ...
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2answers
23 views

Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$.

Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$. Then, which of the following is the best answer? $r_1 = r_2$. $r_1 = 10r_2$ $...
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2answers
64 views

Covariance/Correlation Proof

I'm having a little problem with a statistics problem I am working on. I'm not really sure where to start to prove the two statements. Any help would be greatly appreciated. Let $x$ and $y$ be ...
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1answer
48 views

The mathematics of Correlation is not equal to Causation

In statistics, it is a common practice to say that "correlation does not mean causation", and mostly the proof for this is given by examples. While that is good for the intuition, it's not rigorous. ...
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0answers
37 views

Proof that space of correlation matrices is compact

An $n\times n$ real symmetric matrix is a correlation matrix, if it is positive-semidefinite and all its diagonal entries equal 1. According to most references it is easy to see that the space of ...
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0answers
25 views

Combined Effect size

Is there a way to calculate the effect size between more than 2 components? For example, if i know the effect size of variable A on C and I also know the effect size of variable B on C, is there a ...
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1answer
26 views

How can I solve $\phi_1$ and $\phi_2$?

Let be $$\rho(1)=\frac{\phi_1}{1-\phi_2}, \rho(2)=\frac{\phi_1^2+\phi_2(1-\phi_1)}{1-\phi_2}$$ How can I solve $\phi_1,\phi_2$? My idea: $\rho(1)=\frac{\phi_1}{1-\phi_2}\Leftrightarrow \phi_1=\...
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0answers
20 views

Relationship/correlation between data - does it exist?

Data I refer to in this question Some analysis has been conducted for my business by an external company. The data, as it stands, only really tells part of the story and doesn't provide any real ...
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1answer
23 views

Can I get $\mathrm{Cov}(X_1, X_2)$ in this case?

I know the values of: $\mathrm{Cov}(X_1,Z_1)=M_1$, $\mathrm{Cov}(X_1,Z_2)=M_1*A$, $\mathrm{Cov}(X_2,Z_1)=M_2*B$, $\mathrm{Cov}(X_2,Z_2)=M_2$ Is it possible to get the value of $\mathrm{Cov}(X_1,...
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0answers
14 views

Bounded Stochastic discrete process

I just came across this stochastic process (link): $dY_t = (a-bY_t)dt + c \sqrt{Y_t(1-Y_t)}dW_t$, where $dW_t$ is a Wiener Process. According to the author under certain conditions this process is ...
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0answers
16 views

Problems about Farlie-Morgenstern family of bivariate CDFs

Hi I am trying to solve the following problem: Let $F_X:\mathbb{R}\to[0,1]$ and $F_Y:\mathbb{R}\to[0,1]$ be unnivariate Cumulative Distribution Functions (CDFs) and suppose $-1\le\alpha\le 1$. Define ...
1
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1answer
29 views

Correlation of three values

I have a data set that considers three values, $x,y,z$. And I have three questions: What's the relationship between $x$ and $y$? What's the relationship between $z$ and $y$? What's the relationship ...
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1answer
44 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. Oh my god! In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle ...
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1answer
36 views

Orthogonality of Two Signals.

My last question's link: Reconciling different definitions of orthogonality However, I failed to understand why they are equivalent. If $f$ and $g$ are real, \begin{align} \int_{<T>}f(t)g(t)~...
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0answers
26 views

How to calculate the correlation between two ratings

Suppose x and z are two persons who rate a classical piece of music y on a five point scale. x rates y $3$ out of $5$ z also rates y $3$ out of $5$ I need to know how much the ratings of x ...
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1answer
48 views

Reconciling different definitions of orthogonality

I want to establish about orthogonality in my mind. I knew the orthogonality of two functions $f$ and $g$ in interval T like the following: $$ \int_{<T>}f(t)g^*(t)~dt=0 \tag{1} $$ where $$ g^*(...
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1answer
21 views

Correlate normal shocks

I am trying to generate some random standard normal variables and correlate them In particular I want: $$ \bf Y \sim \mathcal N(0, \Sigma) $$ where $\textbf{Y} = (Y_1,\dots,Y_n)$ is the vector I ...
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0answers
39 views

Correlation between $X$ and $Y$ where $X$,$Y$ are from i.i.d. standard normals and $X+Y > 0$?

Suppose $Z = X + Y$, where $X$ and $Y$ are independent standard normal random variables. If we generate plenty of $(X,Y)$ pairs and only keep the ones where $Z>0$, what's the correlation between $X$...
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1answer
25 views

What is the correlation between the pairwise differences of 2 bivariate normal random variables? [closed]

Given (X,Y) bivariate normal, $U = \frac{X_i - X_j}{\sqrt2\sigma_x}$ and similarly $V = \frac{Y_i - Y_j}{\sqrt2\sigma_y}$ for any two independent pairs $(X_i, Y_i)$ and $(X_j, Y_j)$. Why is this true $...