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

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-3
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0answers
10 views

Analyze mean in difference in before and after measurements [on hold]

I am trying to decide the best way to measure the realationship in the difference between the before and after measurements of a single group. So say I measure the weights of a group 6 ...
0
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1answer
438 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 ...
1
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0answers
14 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, ...
0
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0answers
27 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 ...
1
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0answers
8 views

Is there any reason that cross correlation would perform well or poorly on sparse binary arrays?

I am using matlabs xcorr to correlate simulated photon count data that has some Gaussian random noise set on top of it and it is working fine when the average value in the arrays is greater than one ...
0
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0answers
22 views

Relationship between distributions of correlations $\rho(X^1,Y^1)$ and $\rho(X^2,Y^2)$ if $X^2=WX^1$, $Y^2=WY^1$ and $W$ is a known stochastic matrix?

I have been stacked for a while with the following problem: Consider two samples of iid observations $X^1=\{X_1^1,\dots,X_n^1\}$ and $Y_1=\{Y_1^1,\dots,Y_n^1\}$ where $X_i^1 \sim \mathcal{N}(0,1)$ and ...
3
votes
1answer
82 views

How to curve fit an unknown function?

I have data which can be described by $y=f(x,z)$ where $z$ varies from 170 ~ 154. Now values given by $ks$ are known sample values that equals value given in the table header, $uks$ are unknown ...
0
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1answer
21 views

Which type of correlation should I use?

I am beginner in statistics. I have excel table with few columns. I would like to find correlation between the variables. I have to make an essay to my boss and he wants concrete answers. I searchin ...
1
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1answer
65 views

Cross Power Spectral Density from Individual Power Spectral Densities

Let $X$ and $Y$ be two zero-mean, wide-sense stationary random processes. The power spectral density of a process is the Fourier transform of the process's auto-correlation function. The cross power ...
0
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1answer
20 views

Is it valid to get a correlation between moving averages?

I have a 10 day moving average of one set of return data for one stock and a ten day moving ave of another stock. 400 data points and correlating 390. Can I now get a correlation between the two or ...
0
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0answers
22 views

Independent and Identically Distributed Probability Question

Let $\{X_a\}_{a\in \mathbb{Z}}$ be i.i.d random variables with mean $0$ and unit standard deviation. For $\left(d_0, d_1, d_2, \dots, d_k\right)$, a sequence of $k$ real numbers and $b\in ...
3
votes
2answers
127 views

Correlation of Proportions

To introduce my question, here is a small simplification for consideration: Let $X,Y$ be independent random variates, each with finite mean and variance. Interestingly, ...
0
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0answers
16 views

Let $U=2X$ and $V=-3Y$. Find Correlation (U,V) given Correlation $(X,Y)=0.8$.

Let $U=2X$ and $V=-3Y$. Find Correlation (U,V) given Correlation $(X,Y)=0.8$. My Steps: $$\begin{align} Correlation (U,V) & = \dfrac{Cov(U,V)}{\sqrt{Var(U)\cdot Var(V)}} \\ & = ...
2
votes
1answer
56 views

Wedge Product Formula For Sine. Analogous Formula Generalizing Cosine to Higher Dimensions?

So I was day dreaming about linear algebra today (in a class which had nothing to do with linear algebra), when I stumbled across an interesting relationship. I was thinking about how determinants are ...
5
votes
3answers
3k 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 ...
0
votes
1answer
26 views

Independent variable vs. Uncorrelated variable confusion. How do I interpret this?

I'm reading Time Series Analysis and Forecasting by Example by Søren Bisgaard and Murat Kulahci and I'm having trouble conceptualizing a particular passage and it's bugging me enough that I can't move ...
1
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0answers
17 views

FFT of k*k matrix from FFT of a j*j matrix

FFT of matrix a j by j matrix, A $\begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}$ = $\begin{bmatrix}10 & -2\\-4 & ...
1
vote
2answers
37 views

What is the rigorous justification for using inner products as a function of similarity between two vectors?

In machine learning, it is a common thing to define similarity measures, specially using the so call Kernel function. Kernel functions are defined though through inner products of feature vectors: ...
0
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0answers
11 views

independence in rank vs independence in correlation

while watching a coursera lecture on lecture on correlation , at around 5:00 , the instructor says that if two random variables X, and Y are independent then there correlation will be zero, but the ...
1
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0answers
24 views

Increase the probability of correct prediction using multiple regression

First off let me begin by saying that I'm brand new to statistics and I would appreciate it if you could dumb down any answers for my problem. I am trying to create a general prediction of how much a ...
4
votes
1answer
200 views

Uncorrelated but not independent random variables

Is it possible to construct two random variables $X, Y$ both of them assuming exactly two non-zero values which are uncorrelated, i. e. $\mathbf{E}[X \, Y] = \mathbf{E}[X]\,\mathbf{E}[Y]$, but not ...
1
vote
1answer
21 views

Conditional Probability Distribution for two Discrete Uniform Random Variables with given Correlation Coefficient

I consider a problem with two random variables $X, Y \sim Unif\{a,b\}$, for which I want to set a correlation coefficient $Corr(X,Y)=\rho$. Now, I am interested in the conditional probability mass ...
0
votes
1answer
335 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 ...
0
votes
1answer
612 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
23 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 ...
0
votes
1answer
780 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 ...
1
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0answers
27 views

Correlation Matrix using Matrix Algebra, not the Same as Result from Excel

I am attempting to verify a calculation found at another question on this site. The formula is said to provide a correlation matrix using q = D-1ED-1 where q is the correlation matrix; E is the ...
5
votes
2answers
33 views

correlation between $\sum_{i=1}^{98}X_i$ and $\sum_{i=3}^{100}X_i$

Let $X_1,...,X_{100}$ be iid $N(0,1)$ random variables. The correlation between $\sum\limits_{i=1}^{98}X_i$ and $\sum\limits_{i=3}^{100}X_i$ is equal to (A) $0$ (B) $\dfrac{96}{98}$ (C) ...
5
votes
1answer
7k views

Generate Correlated Normal Random Variables

I know that for the $2$-dimensional case: given a correlation $\rho$ you can generate the first and second values, $ X_1 $ and $X_2$, from the standard normal distribution. Then from there make $X_3$ ...
1
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0answers
16 views

How to find covariance of sample mean and sample standard deviation

I have a question to find the covariance of sample mean and sample standard deviation based on the following: I have tried something on my scratch paper, but for some reason, I cannot upload on ...
0
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0answers
37 views

Covariance and correlation of summations of independent random variables

This is the problem: There are 2n − 1 independent random variables X1, 𝑋2, ... , 𝑋2𝑛−1. The expectation E(Xi) is μ for all i = 1,...,2n−1. The variance Var(Xi) is σ2 for all i = 1,...,2n−1. Let ...
0
votes
1answer
35 views

Linear Regression and finding Correlation Coefficient

In a Simple Linear Regression $y= \alpha + \beta x + \epsilon $, we gather this information: $S_y=20, S_x=5, \widehat{\beta} = 0.2 $ how I could find Instance Correlation Coefficient between x and ...
1
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0answers
32 views

Covariance matrix using squared exponential function

I'm writing down the covariance matrix $K$ of a vector X using squared exponential covariance function, and then evaluating the determinant of the matrix $K$. Let's say i add a new point to $X$ , and ...
0
votes
0answers
6 views

given means and deviation find the correlation

I have some problems in effect size calculation for meta analysis. I want to use the difference between mean gain scores and standard deviation of gain score as the effect size. I need to calculate ...
0
votes
0answers
10 views

Find normal random variables from independent standard normal variables with correlation matrix

I'm trying to find three independent standard normal variables from three normal random variables using a correlation matrix. So far, I have decomposed the problem using the matrix's cholesky ...
0
votes
0answers
7 views

(bounds on) mean of correlation matrix

Let $C\in\mathbb{R}^{p\times p}$ be a correlation matrix, that is a positive (and thus symmetric) definite matrix with main diagonal elements equal to $1$ and off-diagonal entries in the interval ...
1
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0answers
12 views

Augmenting a matrix with a highly-incorrelated column

Consider a binary matrix: $$\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 &1 \\ \vdots & \vdots &\vdots \\ 1 & 1 & -1\end{pmatrix}$$ with a random distribution of 1 and -1 ...
1
vote
1answer
18 views

Given f(x) and two correlated random variables x & y, how do I estimate the correlation of f(x) & f(y)

I have a smooth continuous well-behaved function f(x), where f(x) is positive and mononically increasing with x, and x is positive real continuous variable. Given the mean, variance, and correlation ...
2
votes
2answers
1k views

help understanding step in derivation of correlation coefficient

I'm looking to understand the starred step in the derivation below (also, if someone could help with the LaTex alignment, I'd appreciate it). The regression line is $y= b_0 + b_1 x$, where $b_0$ and ...
0
votes
0answers
50 views

Estimating Percentile Ranks - Correlation

I'm going to type out the question, run the answers I've gotten so far by you, and then ask about what I'm having issues with. Question: In a large statistics class the correlation between midterm ...
1
vote
0answers
8 views

Convergence under rank correlation

I have a following setup: Let $c\in{\Bbb R}$, $R^2\in [0,1]$ and $\Psi,\varepsilon_1,\varepsilon_2,\ldots$ independent random variables on a probability space $(\Omega,{\cal A},{\Bbb P})$. Define the ...
0
votes
0answers
21 views

Error of 2 correlated variables, proxied as random variables

Disclaimer: my 1st question in math.stackexchange (usually in stackoverflow !), and non-English speaker. I'm trying to solve this problem for an arbitrary no. of variables, with multiple categories ...
-1
votes
1answer
21 views

increment of Brownian motion squared [closed]

$(W_t)_{t \geq 0}$ is Brownian motion, assume t>s, does $E[(W_t-W_s)^2W_s^2]=(t-s)s$ ? In other words, are $(W_t-W_s)^2$ and $W_s^2$ independent?
0
votes
1answer
35 views

Given an unfilled pmf, How to compute the Correlation coefficient?

This is the format in which I was given the PMF. Given this pmf $$\begin{array}{lll} x&y&f_{xy}(x,y)\\ \hline 1&1&.25\\ 1&2&.25\\ 2&1&.25\\ 0&0&.25 ...
0
votes
0answers
10 views

Why is pure sample covariance a bad metric to understand the degree of correlation between two variables?

Covariance helps you understand how variables are linearly related. Would it be possible to have two pairs of variables in a deterministic relationship (i.e. linearly correlated variables) that have ...
1
vote
0answers
29 views

Two forms of cross-correlation

Wikipedia and MATLAB defines cross-correlation in this way. In time series analysis (P21), it defines cross-correlation upon cross-covariance: Let $\{X_t\}$ and $\{Y_t\}$ be two time series, ...
0
votes
0answers
16 views

Correlation to a Curve

If I have a problem with data correlation. I have a quadratic $x$/$y$ model that is representative of a process, could I use it to find an equivalent value of $y$ at a given $x$ if I have an $x$ and ...
0
votes
0answers
9 views

An algebraic relationship between inverses of the correlation and covariance matrices

Suppose that we have $p$ random variables $(x_1,\ldots,x_p)$. Stack them together as $x=(x_1,\ldots,x_p)'$ and let $V$ be the covariance matrix of $x$ and $R$ the correlation matrix. Suppose that $V$ ...
2
votes
1answer
57 views

Simulate correlated $\chi^2$ distribution

I understand that when one have multiple independent variable that follows $N\sim(0,1)$, denoted as $A$ if we have a correlation matrix $R$, we can generate correlated variables $B$ that are normally ...
0
votes
1answer
29 views

Don't understand dirac delta function for white noise?

Say we have stochastic differential equation $\frac{dx}{dt} = n(t)$ where $n(t)$ is a noise process. $n(t)$ has a correlation function $R(t - t') = <n(t)n(t')>$ If the noise process is white ...