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

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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 ...
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74 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 ...
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59 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 ...
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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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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 ...
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74 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( ...
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0answers
75 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) = \#\{ ...
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1answer
857 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 ...
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1answer
124 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 ...
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1answer
70 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 ...
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32 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 ...
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1answer
297 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 = ...
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94 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 ...
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0answers
36 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 ...
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1answer
90 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 ...
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0answers
130 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 ...
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0answers
43 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 ...
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1answer
2k 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 ...
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2answers
176 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 ...
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1answer
101 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?
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2answers
6k 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 ...
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1answer
196 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 ...
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736 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 ...
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2answers
204 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 ...
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Can correlation dimension of an attractor exceed the dimension of the space?

Here is the definition of the correlation dimension: http://en.wikipedia.org/wiki/Correlation_dimension Is there a proof that the correlation dimension cannon exceed the dimension of the space?
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3answers
634 views

Finding a Correlation between Bernoulli Variables?

Let X and Y be Bernoulli random variables. We don't assume independence or identical distribution, but we do assume that all 4 of the following probabilities are nonzero. Let a := P[X = 1, Y = 1], b ...
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Is correlation (in some sense) transitive?

If we know that A has some correlation with B ($\rho_{AB}$), and that B has some with C ($\rho_{BC}$), is there something we know to say about the correlation between A and C ($\rho_{AC}$)? Thanks.
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1answer
290 views

Expectation of product of correlated Brownian motions at different time points

Given the information about the correlation of two Brownian motions as $E[dW_1 dW_2] = \rho dt$ and knowing that $E[W_1(t)W_1(t')] = \min(t,t')$, I want to compute $E[W_1(t)W_2(t')]$ I interpret ...
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1answer
38 views

Correlation of two Binomial RVs

Suppose a coin is flipped 30 times. Let X = #heads in first 20 flips, Y = #heads in second 20 flips. I want to find Corr(X, Y). I am only confused on how to find Cov( X, Y) = E[ XY] - E[ X]E[ Y], ...
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1answer
46 views

Correlation formula for discrete phenomena in time

I need a statistical formula to capture a particular phenomena that I need to model in software. I have a light that can be on or off. When turned on, it can be one of many colors (for example, ...
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1answer
58 views

Compute for Cov(X,Y) and Correlation(X,Y)

Let $(X, Y)$ be uniform on the half disc $D = \{(x, y) : 0 < y, x2 + y2 < 1\}$. How should I approach this problem. Should I solve double integral with inside goes from $-\sqrt1-x^2$ to ...
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38 views

Compute correlation between two random variables

A coin is flipped 100 times. Let $X$ be the number of heads in the first 70 flips and $Y$ the number of heads in the last 50. Compute the correlation of $X$ and $Y$. Here's my attempt: ...
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Interval of non-uniformly distributed set of numbers adjusted that it properly excludes extremes

Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution: numbers 1, 2 and 3 about 20 occurrences number 6 has 2 occurrences and number 9 has only ...
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1answer
234 views

Random Variable Problem w/ variance

Three zero mean, unit variance random variables X, Y, and Z are added to form a new random variable, W = X + Y + Z. Random variables X and Y are uncorrelated, X and Z have a correlation coefficient of ...
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How can I simply prove that the pearson correlation coefficient is between -1 and 1?

For building a recommendation system, I also use the Pearson correlation coefficient. This is the definition: $r(x, y)=\frac{\sum_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n ...
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Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
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61 views

Redundancies in covariance matrix

We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
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1answer
2k views

Correlation coefficient of Wiener process

First, I'm not majoring mathematics. I'm studying economics and during reading a thesis I can't understand the 'wiener process' well. I read some books about it and understand the main idea and ...
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2answers
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Solving for the covariance of a joint pdf

Let X and Y have a joint pdf given by $f_{x,y}(x,y) = \begin{cases} 1 & \text{if } 0<y<1,\text{ } y-1<x<1-y \\ 0 & \text{otherwise} \end{cases}$. (a) Find Cov(X,Y) and ...
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105 views

Expectation of random variables

a) Show that $E\{X-E(X)\} = 0$ for any random variable $X$. b) Use the result in part (a) and the following equation to show that if two random variables are independent then they are uncorrelated, If ...
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1answer
82 views

A question about Pearson correlation coefficient

Suppose that we have two vectors $x=(x_1,\ldots,x_n),y=(y_1,\ldots,y_n)$ is the following correct about their Pearson correlation coefficient? $\operatorname{corr}(x,y)=\operatorname{corr}(x+a,y+b)$ ...
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1answer
45 views

Curve Fitting and Multiple Experiments

Say I do an an experiment 5 times, each of which gives you a list of data points. Do I fit a curve to each one separately and then average the parameters and their uncertainties? Or do I take the ...
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82 views

When does convergence in distributions inply convergence in covariance?

Good Morning. Let $(X_n)_n$ and $(Y_n)_n$ be sequences of random variables converging in distribution respectively to $X$ e $Y$. Suppose $X_n,Y_n$ are equally distributed but dependent for all $n$, ...
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Finding correlation of data with potentially hidden time lags

Let's say I have few independent variables plus multiple observables that I monitor over time for a system. I'd like to find out if there is any correlation between the observables and any of the ...
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1answer
62 views

Multivariate Gaussian density from singular covariance

I have a multi-dimensional (~600dim) sample from which I determine its covariance matrix. The determinate of the covariance is 0. The sample does not show strong correlations when plotting 2 ...
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1answer
220 views

Finding the joint distribution of a random process with memory

I'm modeling a digital system as a random process and attempting to solve for the autocorrelation in order to arrive at the power spectral density of the process. The system is as follows: At any ...
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1answer
97 views

Autocovariance of a given stochastic process?

I need to find the autocovariance $C_{YY}(t,s)$ of the stochastic process $Y(t) = t^2 X(t) -2X'(t)$ where $C_{XX}(t,s) = e^{-t^2 -s^2}$ is given. Using known properties I can calculate the ...
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136 views

Why is this convolution true?

I am a little puzzled by how the following summation has been written as a convolution, with one of the inputs reversed in time. Consider the following sum on the LHS, and the convolution on the RHS. ...
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47 views

Question on change of variables during convolution/correlation

I am trying to understand how the following two statements are equivalent: $$ \sum_{l=-\infty}^{\infty} h^*[l] \ R_{xx}[m+l] = \sum_{i=-\infty}^{\infty} h^*[i-m] \ R_{xx}[i] $$ I get that we made ...
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A vector with fixed correlation with existing vector, is it always possible?

Suppose we have a known vector $X$ in $R^n$, and for any vector $Y$ in $R^n$, we impose on it the restriction that it must have a fixed correlation coefficient $r$ with $X$: \begin{align*} ...