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

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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 ...
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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, ...
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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 ...
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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 $V$ ...
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1answer
17 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 ...
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1answer
37 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 ...
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3answers
67 views

Correlation of uniform variables

Let $X$ and $Y$ be independent random variables, $X,Y \sim unif(0,1)$. Let $U = \min \{X,Y\}$ and $V = \max\{X,Y\}$. Find the correlation coefficient of $U$ and $V$. I think we can assume that $U = ...
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How can I get a Covariance Matrix from Mean and Variance?

this may be a very basic question. I have the mean and variance for 12 lognormal distributions: ...
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How to calculate correlation between discrete data points?

I understand there are numerous correlation algorithms, but I wanted some more suggestions on what to use. Here is my situation: I have one list of discrete data points, that I'll call "ideal" case ...
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1answer
16 views

Relation between Regularization and correlation

I was going through Chapter 3 (page 63 bottom) of Elements of Statistical Learning. While explaining regularization in ridge regression authors make the following statements. "When there are many ...
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Coefficient of variation vs Pearson's rho

If you get the same outcome in case of Pearson's rho when comparing interval/ratio statistics, but the intervals/ratios are different, is it possible to use the coëfficiënt of variation to say more ...
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centering two variables X and Z makes cov (X,XZ) = 0

I've read that centering two normal (or symmetrical) variables $X$ and $Z$ affects correlation of centered $X$ with interaction term $X\cdot Z$ in such way, that this correlation $cor(X-EX, X\cdot Z)$ ...
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How to describe the correlation between two non-random variable mathematically?

As we all know, correlation is a statistical relationship between two random variables. However, if there are two non-random variables, is there correlation between them, if it has, how to describe it ...
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A stochastic process is generated as follows: we assign the value 1 to a head and the value 0 to a tail. Start at n=0, Compute Rxx(0,0) and Rxx(2,3)

I am kind of confused here, since autocorrelation describes the correlation between values of the process at different times, but for the first case, it is at the same time. I got that ...
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2answers
45 views

Correlation between two variables

Assume $X_1$, $X_2$, $X_3$,..., $X_n$ are i.i.d, say that $Y_1$ = $X_1^2/\sum_i X_i^2$ and $Y_2$ = $X_2^2/\sum_i X_i^2$, how to calculate the correlation between $Y_1$ and $Y_2$ or prove that they are ...
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1answer
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Correlated explanatory variables in linear regression

Is it any reason to assume that if two strongly correlated explanatory variables have impact on response that regression coefficients for these variables have the same signs ? Could such assumption be ...
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1answer
21 views

Interpreting high p value and low correlation value

I am trying to run regression on financial data in R. I am new to regression analysis so I am finding it to difficult to interpret certain scenarios. I have the code as follows: Regression analysis ...
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Formula for the correlation between two different variables

"Jon planted a plant. When the plant grew to 4 centimeters of height he decided to start to measure how much the plant grew each week. Here's the result Week 0: 4 cm. Week 1: 6 cm. Week 2: 10 cm. ...
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Comparing two vectors based on order and ranking?

What I want to do is compare the ordering of variables determined by the ranking of each variable. For example: Say, I have a rating system that is made up of 5 different ratings - Excellent Good ...
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1answer
27 views

Relation between Correlation and Convolution

We have two functions of time $f(t)$ and $g(t)$, for which convolution and correlation are defined as following: Convolution: $(f(t)\ast g(t))(\tau) = \int_{-\infty}^\infty{f(t)g(\tau-t)dt}$ ...
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33 views

Random Matrix Theory Noise

Hello and Merry (past) Christmas! I am new to random matrix theory, was reading an article about how to improve a correlation matrix (for portfolio optimization). And everywhere i see this "noise ...
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Why is the maximum value of cross-correlation achieved at similar section?

I'm a bit confused and probably need some sleep. When trying to find a short signal inside a long one (or the delay), it's almost a trivial fact that we should look for the maximal valued coefficient ...
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Correlation of variables sets

There are a number of entities. Each entity is represented as three sets of numbers. Each set consists of the same number of parameters and describes behaviour of the entity in the specific ...
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Multiple variables correlation

There are a number of entities. Each entity has three sets of parameters. Each set of parameters describes entity behaviour in a specific system. The problem is to find mathematical method that would ...
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Partial Correlation Coefficient

I have the following questions on computing the correlation coefficient. Let us say we have two discrete random variables $X_1$ and $X_2$, where $X_1$ has $n_1$ outcomes and $X_2$ has $n_2$ ...
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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 ...
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1answer
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Given an unfilled pmf, How to compute the Correlation coefficient?

This is the format in which I was given the PMF. Sorry for the messy table, don't know how else to make a table. Given this pmf $x$$y$ $f_{xy}(x,y)$ 1       ...
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1answer
18 views

Can I sum variances to a compound variance?

Say I have three locations A,B,C and I have a person going from A to B and measure the time it takes. Same for B to C. Let the variance of the time it takes for the path AB be a and for BC b. Is it ...
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1answer
34 views

Approximate as Independent Identically distributed

If $N$ random variables are identically distributed but weakly correlated, in what condition we can approximate them as independent identically distributed (iid) ? I saw an old paper where based on ...
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1answer
38 views

The autocorrelation function - the result in the form of a vector.

I've implemented the autocorrelation function in Python according to the normalized autocovariance function for discrete signals, i.e: ...
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51 views

The product of a normal and Bernoulli variables, independent from each other

Let $X\sim N(0,1)$ and let $Z$ be a random variable independent of $X$ such that: \begin{equation} \Pr(Z=z) = \begin{cases} \frac{1}{2} & \mbox{if $z = -1$ or $z=1$}, \\ \\ 0 & ...
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different way to compute power spectral density

I am writting a piece of code to compute power spectral density (psd) of a signal and wanted to compare two approaches : compute the FFT of the signal and square its amplitude compute the biased ...
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Product of two random variables - Resulting Distribution and Correlation?

Let $X \sim \mathcal{N}(0,1)$ and let $Z$ be a random variable independent of $X$ such that \begin{align*} P(Z=z) = \begin{cases}\frac{1}{2} & z=-1\\ \frac{1}{2} & z = 1\\ 0 & ...
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I'm confused on how to use chi squared for the correlation between age and reaction time

I am doing my IB maths internal assessment and I am confused on how to specifically carry out chi squared with my given data. I will try to explain this quite plainly so the image is clear. I am ...
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1answer
26 views

If two functions are even, then X and Y are uncorrelated

I Need some help: Let $Y=h(X)$ be a real square integrable function and X has a density function $f$. Show: If $f$ and $h$ are even functions then $X$ and $Y$ are uncorrelated (but generally not ...
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correlation coefficient is over 0.7

"correlation coefficient can be over 0.7 then we can say Two factors have some strong relation. Then What is the 'reason' that we can say like that? Explain it." I got that problem and I really dont ...
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1answer
33 views

Proof of Correlation Coefficients

Good evening, I have a problem with an exercise: Let $X$ and $Y$ be two real square integrable random variables with var$X>0$, var$Y>0$. The correlation Corr$(X,Y)$ quantifices how far $X$ and ...
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1answer
38 views

Inverse Z transform of symmetric function $R_{x}(n) = 3\cdot (0.8)^{|n|}$

On Z-transform table, most of the pairs are only valid for $n≥0$. My question is to find PSD (Z transform) of $$R_{x}(n) = (0.8)^{|n|}$$ Note that $n$ is an integer span from $-\infty$ to ...
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Relationships between numbers

So I'm working on this idea that I had, Example: There are 3 people in a room how many hand shakes would it take for all of them to hand shake. The answer is 3. I've done the work up to 8 ...
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1answer
23 views

Three pairwise uncorrelated random variables

Given $\xi$, $\eta$, $\zeta$ are pairwise uncorrelated, can we say, that $E(\xi\eta\zeta) = E\xi E\eta E\zeta$?
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Why does one compute the power spectrum of an image from the Fourier transform of its autocorrelation and from the square of its spectrum?

image: f(x,y) fourier transform of f is F(u,v) my Goal is to compute its power spectrum. [denoted by P(u,v)] the first way to compute is by using the magnitude of fourier transform: ...
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1answer
15 views

Help with correlation question? How to solve this?

Let $X$ and $Y$ be random variables and $a,b$ $\in$ $\mathbb{R}$ such that $a \neq 0$. If $Y = aX + c$, then show that corr($X, Y$) = +1 or corr($X, Y$) = -1.
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Weighted Average of Correlation Matrix

Let $R$ and $Q$ be two correlation matrices of the same size and let $p\in[0,1]$. I'm trying to show that $pR+(1-p)Q$ is still a correlation matrix. I claim that $\sqrt pX+\sqrt{1-p}Y$ is a vector ...
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1answer
24 views

Joint PDF Correlation

In the problem I am given $f(x,y)=2,\ 0 < x < y,\ 0 < y <1$. I'm trying to find the correlation $\rho$ which I know is equal to $$\rho = \frac{Cov(x,y)}{\sqrt{Var(x)Var(y)}}$$ ...
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1answer
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Computing the expected value of the product of two discrete variables

I didn't know why I compute $E(XY)$ wrongly. $$X=(1, 2, 0.5, -1),\qquad Y=(-2, 1, -0.5, 2).$$ $$E(XY) = \frac{-2 + 2 -0.25 -2}{4} = -0.5625\text{ (incorrect)}$$ because ...
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Size of sample and correlation coefficient

$X$ and $Y$'s correlation coefficient is $r=0.5$. What is the size of sample when the correlation is significant at $\alpha=0.05$ with two sided test? Is there a more "formal" way to solve this ...
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Transform two correlated random variable to independent variables without knowing correlation

I am thinking about this interesting question which arises in the following realistic setting. For example, in one medical experiment one drug and one placebo are applied to two randomized groups of ...
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72 views

Partial proof for correlation coefficient formula?

I've been working to prove the formula for the correlation coefficient, since asking my last question yesterday (Meaning of denominator in correlation?). If this post in any way violates any ...
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165 views

Meaning of denominator in correlation?

I can't quite grasp the meaning of the denominator in the correlation coefficient. $$\frac{\sum(X - \bar X)(Y-\bar Y)}{\sqrt {\sum (X-\bar X)^2\sum(Y-\bar Y)^2}}$$ What exactly am I dividing with, ...