# Tagged Questions

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

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### 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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The following journal article seems to suggest Over a $5$-minute period there is a correlation between returns The average return is $0.037\%$ The average daily gain is $0.59\%$ Would anyone know ...
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Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors). Then Pearson's r reduces to Covariance: \rho(X,Y) := \frac{... 0answers 20 views ### Change eigenvalues of correlation matrix and transform into original basis I use the Random Matrix Theory to filter out the information from the correlation matrix that is associated with noise - Marcenko Pastur band. That is straight forward. Then I follow Rosenow, Bernd, ... 1answer 24 views ### How to find an equation that describes a non-linear correlation of multiple parameters I tried to search for this problem but I don't know what exactly I'm looking for. I found some empirical parameters that correlate but not linearly. An example follows: Y_1 and Y_2 are the values ... 0answers 10 views ### Does Averaging the score from correlation across multiple variables yield a more accurate correlation score? This may be a beginner question but I am making a application which I using to do correlation research to be used in financial markets. The application pulls in different data sources and compares ... 0answers 31 views ### Estimator for the correlation coefficient My question is related to the correlation between random variables X and Y, where (X,Y) is bivariate normal. My understanding is as follows. The correlation coefficient is \rho=\dfrac{\... 0answers 22 views ### Hypothesis testing for the correlation coefficient My question is related to the correlation between random variables X and Y, where (X,Y) is bivariate normal. My understanding is as follows. The correlation coefficient is \rho=\dfrac{\... 0answers 30 views ### Explanation of “When two functions a(x) and b(x) are not correlated on domain X, they can be separately integrated” Hy everyone, I was reading this paper https://hal.inria.fr/hal-00942452v1/document , and I came up with a statement that I don't fully understand, nor could I found any info on it, so decided to ask ... 0answers 9 views ### Is Markov Chain property true for correlated inputs? I have a finite state machine (FSM). At time k, state is \theta^k and input is x^k. The next state \theta^{k+1} and output y^k are completely determined by \begin{align} \theta^{k+1} &=... 1answer 16 views ### Predict value of random variable B if value of random variable A and correlation is known Intuitively it is clear that if I have two variables A, B \sim \mathcal{N}(\mu, \sigma) and I have \rho_{A,B}=-1, then if some sample a of A is x, then some sample b of B is \mu-x ... 0answers 21 views ### Correlation matrix for linear combination of two variables and combination coefficients I have a question: I have N different linear combinations of two random variables X,Y (distribution is strictly speaking unknown, but probably either normal or log-normal, and shall be the same ... 1answer 32 views ### Why is the regression line an estimate of the average value of y for each value of x? The regression line, passing through the point of averages with a slope equivalent to r, is said to be a good estimate of the average value of y for each value of x. I can see why this is the cases ... 0answers 7 views ### What is the relationship between regression line and graph of averages? Why is the regression line regarded as a smoothed version of the line of averages, and why is it that when the graph of averages falls on a straight line, that line is also the regression line? 1answer 19 views ### Best coefficient between two data sets I want to determinate a sensor coefficient but I struggle with a basic math problem... Here are my values : ... 1answer 32 views ### Creating custom correlation matrix I'd like to be able to create a matrix like the one below to be a correlation matrix. Trouble is, I cannot ensure it is positive definite, hence cannot use Cholesky factorisation, which I need to draw ... 1answer 1k 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 ... 0answers 47 views ### How can this double summation be solved? I have to calculate the following expectation\mathbb{E}\left[\left(\frac1M\sum\limits_{i=1}^MX(i-n_1-M)\right)\left(\frac1M\sum\limits_{j=1}^MX(j-n_2-M)\right)\right]$$where M, n_1 and n_2 ... 0answers 27 views ### Find the autocorrelation of y[n]=x[2n] in terms of the autocorrelation of x Find the autocorrelation of y[n]=x[2n] in terms of the autocorrelation of x, given that the autocorrelation of x is:$$R_{xx} = \frac 1{n\pi}\sin\left(\frac {\pi}{2}n\right).$$I've tried to ... 1answer 23 views ### The relation of correlation coefficient of the sum of two vectors. Does the correlation coefficient of the sum of two vectors between the correlation coefficient of each of them. Suppose I have three vectors x_1,x_2,x_3. The correlation coefficient of x_1 and ... 0answers 13 views ### Pearson Correlation I have two matrices, which are square but of different size. I want to find correlation between data which is stored in these two matrices. It seems Pearson Correlation Coefficient is applicable for ... 1answer 45 views ### Variance of sum of linear combination I want to calculate the variance of a sum of linear combinations, so$$\operatorname{Var}\left(w'R_1 + w'R_2\right)$$where w is a N\times 1 vector and both R_1 and R_2 are N\times 1 ... 0answers 16 views ### Correlation of an integral Assuming that a(x) is a random variable and correlation \xi(x_1,x_2)=\langle a(x_1)a(x_2)\rangle is known (where angular bracket denote statistical averaging), it it possible to write the ... 2answers 71 views ### Variance of the sum of correlated variables If the variance of two correlated variables is:$$Var(r_1+r_2)=\sigma^2_1+\sigma^2_2+2\textrm{cov}(r_1,r_2)=\sigma^2_1+\sigma^2_2+2\rho\sigma_1\sigma_2$$where r_1 and r_2 are vectors, then what ... 1answer 34 views ### Given the correlation matrix, estimate the value of a random variable based on the value of other random variables. [closed] A process generates N random variables (X_i \mid 1 \leq i \leq N). The process is run K times, and the values of each random variable X_i is observed. Based on this data, the following ... 2answers 112 views ### Is a correlation matrix with positive determinant PSD? Please note: I'm not interested in the difference between positive definiteness and semi-definiteness for this question. A correlation matrix is a symmetric positive semi-definite matrix with 1s down ... 1answer 42 views ### Can I ignore multicolinearity problem if all the regression coefficients are highly significant? Can I ignore multicolinearity problem if all the regression coefficients are highly significant? My data is large enough and all the resulting coefficients are significant enough in less than 0.01 ... 1answer 1k 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 ... 1answer 27 views ### coefficient of determination: absence of cross products [closed] With regard to the coefficient of determination, why is the total variation equal to the sum of the explained variation and the unexplained variation and there are no cross-products? 0answers 13 views ### statistical test for comparison of time series of rare events I have two time series of a binary variable which assumes value 1 if an event happens and 0 otherwise. Both series report the occurrence of the same event and are not necessarily equal because the ... 0answers 28 views ### Show that E(\mathrm{var}(Y|X)) \leq (1 - \mathrm{corr}(X,Y)^2) \mathrm{var}(Y) Expectation of conditional variance (Exercise 4.6.7 from Grimmett and Stirzaker): Let X and Y be random variables with correlation \rho. Show that E(\mathrm{var}(Y|X)) \leq (1 - \rho^2) \mathrm{... 1answer 49 views ### How to simulate a delta-correlated random process I'm trying to do the simulation described in the paper attached, but there is something I don't understand. The author says that the random variables which satisfy the relation (Eq. (4) in the paper) ... 1answer 31 views ### What is a deviation vector? LINEAR ALGEBRA: I've looked online for this and can't find anything... What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?) Here is ... 3answers 72 views ### Find ratio / division between two numbers I am reverse engineering custom software for a stepper motor. The original software eases in and out of any motion, and the duration of the ramping up to speed is directly related to the speed that ... 1answer 14 views ### Negative autocorrelation values Autocorrelation is informally defined (Wikipedia article) as "the similarity between observations as a function of the time lag between them". I create the following time series in MATLAB: ... 0answers 10 views ### Finding a correlation between days on the market and seller rank If you are given two variables, D = Days since a product was launched on amazon B = Bestseller Rank among a specific amazon product category How could you compare / rank a list of products based ... 1answer 27 views ### How to find point in polynomial regresion I have the following data set: ... 0answers 6 views ### Periodic Cross-Correlation vs Aperiodic Cross-Correlation I am doing research in spread spectrum communication, and many papers frequently use the terms Periodic Cross-Correlation and Aperiodic Cross-Correlation. However, I cannot find a clear definition of ... 0answers 14 views ### X and Y are standardized r.v.s. Find a,b,c,d such that Z=aX+bY and W=cX+dY are uncorrelated but still standardized. Let X and Y be standardized r.v.s (i.e., marginally they each have mean 0 and variance 1) with correlation \rho \in (−1, 1). Find a, b, c, d (in terms of \rho) such that Z = aX + bY ... 1answer 37 views ### Change of Uniform Continuous Variable Let X be a U(-1, 1) random variable, we define Y = X^4. Calculate the correlation coefficient between both variables. Are they uncorrelated? PS. I don't know how to use MatJax equations, I'm ... 2answers 36 views ### How does the Pearson correlation coefficient change under rotations I was reading on wikipedia about the pearson correlation coefficient. Assuming the data has zero mean it can be written as$$ \rho = \frac{ \sum x_i y_i } {\sqrt{\sum x_i^2 \sum y_i^2}} $$The ... 0answers 13 views ### If all points lie on regression line, how is coefficient of correlation affected? If all points lie on a regression line, what does that mean for the coefficient of correlation? Am I correct to say the coefficient of correlation is either -1, 0 or 1? 2answers 78 views ### Interpretation of correlation (coefficient) In an discussion we were confronted with a very special opinion about correlation in respect of financial assets. The widely used correlation coefficient is used here to give an idea about how ... 0answers 51 views ### How to generate correlated random numbers with specific distributions? After read the answers of some similar questions on this site, e.g., Generate Correlated Normal Random Variables Generate correlated random numbers precisely I wonder whether such approaches can ... 0answers 11 views ### Why does the mean centered autocorrelation have a slope of -1? I'm fundamentally not understanding something about the autocorrelation function (as defined by numpy.correlate). Let's say I create a bunch of random signals s_1, ... 1answer 6 views ### Calculating person product moment correlation coefficient on a 3 X 3 table Usually we are given problems that only involve 2 rows (x and y), but recently saw a problem asking how to compute the correlation coefficient on a table of data that has 3 rows and am not sure how to ... 0answers 13 views ### First and second moments of two correlated functions I am trying to find the first and second moments of the following: k=mk^{-b} where m \sim U[a,b] (discrete) and k^{-b} is a power law distribution I know how to find the first and second ... 0answers 46 views ### Formula of phase correlation If I have two 2D signals, and one is the shift of another. I can propose such schema for define offset via continious Fourier Transform:$$f_2(x,y)=f_1(x-x_0,y-y_0)$$Then$$Ff_2(s_1,s_2)=e^{-2\pi j(...
A fair coin is tossed 3 times. Let $X$ be a random variable representing the number of $H$'s appeared in the first 2 tosses, $Y$ the number of $H$'s appeared in the last 2 tosses, and $Z$ the number ...
I wish to generate normals $X$, $Y$, and $Z$ with the correlation matrix $R$ but with means $0$, $1$, and $2$, as well as variances $4$, $16$, and $25$, respectively. How would you do this?