# Tagged Questions

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

3answers
276 views

### Correlation between variables

I asked this question on stats SE but did not find a suitable answer so far. Maybe someone can help. Given n random variables x1,...,xn (one-dimensional). The following is known (corr() = Pearson ...
2answers
60 views

### Relationship between x and y

Studying a financial model from a third party we see: 36month - 1.2 multipler 48month - 1.3333 multipler 60month - 1.5 multipler I am trying to determine if ...
1answer
179 views

### Use Pearson's correlation coefficient on a matrix

I have a problem to interpret the following formula which is said to be the Pearson's correlation coefficient: r = \frac{N \left(\sum XY\right) - \left(\sum X\right) \left(\sum ...
2answers
924 views

### If two Gaussian random variables are uncorrelated, they are statistically independent

I read in a textbook that when two gaussian variables are uncorrelated, then they are statistically independent? How can I prove that?
0answers
36 views

### Sampling a distribution with restrictions: eliminating the correlation between two variables

I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
1answer
89 views

### Correlations between neighboring Voronoi cells

For a sequence $X_1,X_2,X_3,\ldots$ of random variables, what it means to say $X_1$ is correlated with $X_2$ is unambiguous. It may be that the bigger $X_1$ is, the bigger $X_2$ is likely to be. If, ...
1answer
222 views

### Expectation product of pairwise uncorrelated variables

Suppose I have three uncorrelated random variables $X, Y$ and $Z$ (discrete or continuous) such that $$\newcommand{\Cov}{\mathrm{Cov}}\Cov(X,Y)=0;\quad \Cov(Y,Z)=0;\quad \Cov(X,Z)=0 \tag{$\ast$}$$ I ...
3answers
128 views

### correlated or independent

Let $(X_1, X_2)$ be a randomly chosen pair out of $\{1,2, \ldots, 20\}$ (draw without repetition). Are both events $$E_1:=\{X_1 \geq 8\}$$ and $$E_2:=\{X_2 \geq 12\}$$ positive or negative correlated. ...
1answer
186 views

### indicator variable are uncorrelated, if they are independent?

Is it true that if two indicator variables are independent then they are uncorrelated? If covariance =0 $\Rightarrow$ uncorrelated Does the covariance between indicator variables exist? thx
0answers
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### Correlation and Regression Question

Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are:  \begin{matrix} \text{Test A}(x) ...
0answers
91 views

### Correlated Random Numbers Between A Range

I am trying to generate random numbers within a range say 57 to 107 which are correlated by a factor of 0.8. The numbers are for illustration simplicity only.
1answer
207 views

### 3D correlation visualization?

Incomer per person (x axis) correlates with life expectancy (y axis). These two indicators change over time (z axis). x correlates with y. Moreover, x and y both correlate with z. The question is: ...
1answer
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### Long time scale correlation

I have some EXTREMELY noisy data (standard deviation a is greater than the mean), but plotting it with a 15 data point running average does well to get a visual indication of the trending. I want to ...
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558 views

### Generalized variance

Generalized variance is the determinant of correlation matrix. Does increasing the off-diagonal entries (correlation coefficients) decreases the determinant? Is a proof available? All elements are ...
1answer
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### Pearson's Correlation, for comparing a PRNG?

Other than uniformity tests on random numbers of which can be done with other methods, I had wondered if the result of the Pearson Product Moment Correlation function would be an effective means to ...
3answers
404 views

### Bounds on off-diagonal entries of a correlation matrix

Assume that all the entries of an $n \times n$ correlation matrix which are not on the main diagonal are equal to $q$. Find upper and lower bounds on the possible values of $q$. I know that the ...
1answer
1k views

### What is the standard deviation of multiple correlated random variables subtracted from another random variable?

Wiki states that standard deviation of $X-Y$ is: $$\sigma_{x-y} = \sqrt { \sigma_x^2 + \sigma_y^2 - 2\rho\sigma_x\sigma_y }$$ I have a number (say 3) correlated random variables to be subtracted ...
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136 views

### Calculating the correlation between subsequent values in a stream of numbers

I have a stream of integer values being generated $V_1,\cdots, V_n$ and want to calculate how the value of $V_{n+1}$ is correlated to $V_n.$ I would also like to calculate this at run time as ...
3answers
165 views

### Using Correlation for mouse gesture recognition

I am in need to build a mouse gesture recognition system which will compare given recognition to the the gestures in training data and will say where a given gesture best fits. I am planning to use ...
2answers
3k views

### Calculating the variance of the ratio of random variables

I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is $$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$ but, how do I derive it from "common" ...
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### Intuitive meaning of Pearson Product-moment correlation coefficient Formula

I can't understand the intuition behind Pearson Product-moment correlation coefficient Formula for bivariate data. The formula is : $\rho$ = cov(X,Y)/($S_x$ * $S_y$) where cov is covariance. $S_x$ and ...
2answers
488 views

### How to 'minimize' correlation between series

Hi fellow mathemagicians, let's say that I have 3 series of numerical results (they represent 'drawdowns') : ...
1answer
1k views

### Proving correlation coefficient = 1 or -1 given X and Y=a + bX

Given $X$ and $Y = a+bX$, I have to prove that: If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$. I've gotten to the point where I have:  \rho = \frac{b \cdot \sigma_x }{ ...
1answer
821 views

### Cross correlation in MATLAB HELP

I have values from two sensors stored in two vectors A and B. They both represent values of the sensors at times TA and TB which is stored in two other vectors(since it is not uniform sampling) Both A ...
1answer
141 views

### example on variance of stochastic processes

I saw this expression in a book and I cannot understand how did he get this expression. Suppose $Z_t$ and $D_t$ are some stochastic processes and we have these expressions, \$Z_{t_k} - Z_{t_{k-1}} = ...
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324 views

### Correlation between Beta distributions

I have a Computer Science background and not very knowledgeable in Probability and Statistics. So excuse me if my question,notation, or language is flawed. Anyways, the problems is that we have two ...
1answer
135 views

### What is the characteristic formula for the addition of two lognormal distributions?

If I have two lognormal processes (X and Y) with mean and volatiilty for each and also correlation between the two, what is the characteristic formula of X + Y (i.e. what is the new mean and new ...
1answer
231 views

### Calculate Correlation between 2 values

I have a random vector $X = ( X_1 , X_2 )$ that has a bidimensional normal repartition with mean $0$ and covariation matrix :  \Sigma = \left( \begin{array}{ccc} 1 & q \\ q & 1 ...
4answers
666 views

### Going back from a correlation matrix to the original matrix

I have N sensors which are been sampled M times, so I have an N by M readout matrix. If I want to know the relation and dependencies of these sensors simplest thing is to do a Pearson's correlation ...
1answer
480 views

### Statistics - Correlation between 2 sets of data

If i know the means and standard deviations of 2 sets of data, and i know the slope of the regression line, how can I find the correlation? edit Sample 1 SD: 12.37 Sample 2 SD: 7.00 Slope of ...
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