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

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0
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2answers
128 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 ...
2
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1answer
654 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 ...
0
votes
1answer
228 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 ...
0
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1answer
77 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)}} ...
0
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1answer
62 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
votes
2answers
37 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 $Cor(X,Y) = \begin{cases} +1 &\mbox{if } a > 0 \\ -1 & \mbox{if } a < 0. \end{cases}$ ...
2
votes
1answer
35 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: ...
1
vote
1answer
58 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 ...
1
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0answers
143 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 ...
2
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0answers
30 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: ...
0
votes
1answer
31 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) ...
1
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0answers
23 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 ...
0
votes
2answers
52 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
vote
2answers
45 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
vote
2answers
118 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
vote
1answer
39 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 ...
0
votes
1answer
102 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 ...
0
votes
1answer
43 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
votes
2answers
46 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
votes
1answer
855 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 ...
3
votes
0answers
24 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 ...
0
votes
1answer
338 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 ...
0
votes
1answer
796 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
votes
1answer
30 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
votes
1answer
43 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 ...
1
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0answers
207 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. $n = 3$): ...
0
votes
1answer
41 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 ...
2
votes
1answer
70 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
votes
1answer
57 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 ...
1
vote
4answers
847 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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1answer
1k 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 ...
0
votes
1answer
61 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
votes
0answers
72 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) = \#\{ ...
0
votes
1answer
614 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
vote
2answers
101 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 ...
0
votes
1answer
59 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 ...
1
vote
3answers
30 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 ...
2
votes
1answer
235 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 = ...
1
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0answers
91 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 ...
1
vote
0answers
33 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 ...
0
votes
1answer
81 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 ...
1
vote
0answers
109 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 ...
2
votes
0answers
36 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
votes
1answer
1k 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
votes
2answers
155 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 ...
0
votes
1answer
92 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?
1
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2answers
4k 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 ...
0
votes
1answer
158 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 ...
6
votes
1answer
510 views

Covariance, covariance operator, and covariance function

I am trying to get my head wrapped around this article in Wikipedia. The first definition given there is the covariance of a probability measure $\mathbf{P}$: $$\mathrm{Cov}(x, y) = \int_{H} \langle ...
1
vote
2answers
172 views

If $E(Y\mid X)$ is constant then $X, Y$ are uncorrelated.

Last minute studying please tell me how to: Prove that if the expected conditional expected value of the random variable $X$ given the random variable $Y$ - denoted by $E(X\mid Y)$ - is constant ...