Covariance Definition and 173 Threads

The following question appeared on a practice exam: For f(x,y) = 24xy if 0<x+y<1 , 0<x,y 0 elsewhere find Cov(X,Y) I used Cov(X,Y) = E(XY) - E(X)E(Y) to calculate covariance, with E(XY) = \int^{1}_{0}\int^{1-y}_{0}24x^{2}y^{2}dxdy but for some reason I didn't get the...

I know what gauge invariance is, but I'm not sure what gauge covariance is. Is it that a given field has a gauge covariant derivative? And under which circumstances do we get a field that is gauge invariant but not gauge covariant? And I would appreciate an example (other than the one...

Hi! I'm studying special relativity and relativistic dynamics and I'm struggeling a little bit with the concept of 'covariance' of physical equations. As far as I understand so far 'covariance' is related to the 'form invariance' of the equations of motions in relativity and the concept is...

Suppose vectors X1, X2, ... , Xn whose components are random variables are mutually independent(I mean Xi's are vectors of components with constants which are possible values of random variables labeled by the component indice, and all these labeled random variables are organized as a vector X...

How to get a covariance matrix is well defined, but I don't really know how to use it once obtained. I'm trying to find the best parameters for a data set with a given function. I'm having four parameters a1,a2,a3,a4 and from these parameters I have the covariance matrix. I'm supposed to get...

Homework Statement As part of an assignment, I have to determine propagated error of some function: f(x,t) I did it first with x & t being completely uncorrelated, but now I'm given x as a function of t, x(t), and have to do the same.Homework Equations I know the linear approximation for...

Hi, I am trying to follow this paper: (arXiv link). On page 18, Appendix A.1, the authors calculate a covariance matrix for two variables in a way I cannot understand. Homework Statement Variables N_1[\itex] and [itex]N_2[\itex], distributed on [itex]y \in [0, 1][\itex] as follows...

Dear all, I have a problem in solving covariance of Bivariate Poisson Distribution Let X_i \sim POI (\theta_i) , i = 1,2,3 Consider X = X_1 + X_3 Y = X_2 + X_3 Then the joint probability function given : P(X = x, Y = y) = e^{\theta_1+\theta_2+\theta_3} \frac {\theta_1^x}{x!} \frac...

Demonstrations of Dirac equation covariance state: The Dirac equation is (i γ^{μ} ∂_{μ} - m)ψ(x) = 0. \ \ \ \ \ \ \ \ \ \ [1] If coordinates change in a way that x \rightarrow x' = Lx, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [2] where L is a Lorentz transformation, [1] should...

At the time Schwarzschild derived his solution (1915) he only had a version of the EFE that was not fully coordinate free, he used the equations in unimodular form, and therefore he could only consider the "outside of the star" part of the fully general covariant form we know now. So does a...

Hi folks, I know the covariance matrix and the location of a point, both of which are expressed in Cartesian coordinates. I am going to represent the point in barycentric coordinates, and I would like to represent the covariance matrix for the point in barycentric coordinates as well. Does...

So I need to calculate the square root of the covariance matrix \sqrt{\Sigma_tR\Sigma_t} (the matrix square root, not the element-wise square root). \Sigma_t is a diagonal matrix with the square root of the variance on the diagonal (these values are time dependent) and R is the correlation...

I understand the concept of covariance, relating two complex random (scalar) variables. However, I get confused when I have both deterministic and random variables. Therefore, what I write might make very little sense -- I'm really only looking for any general advice on where to start reading...

I'm trying to study the best approaches to quantum gravity and especially the interactions of quantum and the metric. But first let us settle about the so called "spacetime points". What is the proof that spacetime points can't be composed of any substance but purely an abstract. The often...

I have an (m \times n) complex matrix, \textbf{N}, whose elements are zero-mean random variables. I have a sort of covariance expression: \mathcal{E}\left\{\textbf{N}\textbf{N}^H\right\} = \textbf{I} where \mathcal{E}\left\{\right\} denotes expectation, \{\}^H is conjugate transpose and...

I have a time-varying random vector, \underline{m}(t), whose elements are unity power and uncorrelated. So, its covariance matrix is equal to the identity matrix. Now, if I separate \underline{m}(t) into two separate components (a vector and a scalar)...

I think this is right, just want to double check. Cov(Y1+Y2, Ʃ n i=2 Yi)= Cov(Y1, Ʃ n i=2) + Cov(Y2, Ʃ n i=2 Yi) = 0 + Var(Y2) = σ^2 is this right?

According to Weyl's postulate timelike geodesics should be hypersurface orthogonal, this in itself seems to clash with the GR principle that there should be no physically preferred frame or slicing of the spacetime manifold (general covariance). Usually there is much insistence in textbooks...

Hello all. I have set up a model using the Kalman filter to estimate automobile prices. I'm having difficulty in figuring out how to formulate a prediction covariance matrix based on the model, i.e. given a set y_{new} = y_1, \ldots, y_N of N cars, finding the covariance matrix based on the...

I need to find an approximation of the covariance of a function of a random variable. \Theta1- log[p1/(1-p1)] where p1 is binomial \Theta2- log[p2/(1-p2)] where p2 is binomial I need to find the covariance of \Theta1 and \Theta2 Please- any help will be greatly appreciated

Homework Statement [PLAIN]http://img695.imageshack.us/img695/7551/unledsi.png Homework Equations The Attempt at a Solution I get E[u]=1/3 and E[V]=1, can't get E[UV] to be correct as I do not get the required answer, any help would be greatly appreciated! thanks!

My professor sucks she hasnt gone over mean vector and she expects up to solve this let z1, z2, z3 be the random variables with mean vector and covariance matrix given below mean vector = [1 2 3]T. T = transpose covariance vector 3 2 1 2 2 1 1 1 1 Define the new variables...

The fact that physics laws must have the same form in any reference frame (general covariance) is guaranteed by expressing them in tensor notation (, if possible). Considering also non linear coordinate transformations the tensor transformation rules are defined by means of the partial...

Hi there, I am trying to prove the following. For any random vectors X,Y,Z,W in \mathbb{R}^d and deterministic d\times d matrices A,B the covariance \operatorname{\mathbb{C}ov}\left(X^TAY;Z^TBW\right) can in some way be bounded by the covariance...

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula cov(A) = E[(A - E[A])(A - E[A])^{T}) could someone please...

I have a Gaussian distribution. I know the variance in the directions of the first and second eigenvectors (the directions of maximum and minimum radius of the corresponding ellipse at any fixed mahalnobis distance), and the direction of the first eigenvector. Is there a simple closed form...

Dear All, The bivariate Poisson distribution is as follows, \[ f(y_{s},y_{t})=e^{-(\theta_{s} + \theta_{t}+\theta_{st})}\frac{\theta_{s}^{y_{s}}}{y_{s}!}\frac{\theta_{t}^{y_{t}}}{y_{t}!} \sum_{k=0}^{min(y_{s},y_{t})} \binom{y_{s}}{k} \binom{y_{t}}{k}...

Homework Statement Hi, I need to proof the covariance of the equations of motion under an infinitesimal symmetry transformation. Homework Equations Equations of motion: E_i = \left(\frac{\partial L}{\partial \chi^i}\right) - \partial_{\mu} \left(\frac{\partial L}{\partial \chi^i_{\mu}}\right)...

If X and Y are two random variable , then the covariance between them is defined as Cov(X,Y) = E[XY] - E(X)E(Y) i) Show that Cov (aX + b , (Y + d)) = ac Cov(X,Y) ii) Cov(aX + bY, cX + dY) = ac \sigma_x ^2 + bd \sigma_y ^2 +(ad + bc) Cov(X,Y)

Hi! I´m trying to get an intuition for these concepts and was just playing at home. My thought was to start with a 2-Dimensional ON-coordinatesystem, the xy-plane and do the following: 1. Study the vector with the coordinate (1,1) in this system. Now its cov. and con. coordinates is of course...

Covariance and Invariance We consider the equation: {\frac {{d}^{2} {x^{\alpha}}}{{d }{{\tau}^{2}}}}{=}{-}{{\Gamma}^{\alpha}}_{\beta\gamma}{\frac{{d}{x^{\beta}}}{{d}{\tau}}}{\frac{{d}{x^{\gamma}}}{{d}{\tau}}} The covariant form is preserved in all coordinate systems. But the Christoffel...

Can anyone explain to me the meaning of " the Principle of Covariance"? I find it hard to understand the wikipedia explanation.

Hi all, I thought I posted this last night but have received no notification of it being moved or can't find it the thread I have started list. I was wondering if you could help me understand how PCA, principal component analysis, works a little better. I have read often that it to get the...

I've been reading everywhere, including wikipedia, and I can't seem to find a prove to the fact that the covariance matrix of a complex random vector is Hermitian positive definitive. Why is it definitive and not just simple semi-definitive like any other covariance matrix? Wikipedia just...

Homework Statement Find the Cov(X(t), X(t+s)) where X(t) = N(t+1)-N(t), where N(t) is a poisson process with parameter \lambda. Homework Equations The Attempt at a Solution X(t) should be poisson distributed with mean 1\lambda by stationary increments, and X(t+s) should be poisson...

Hello Buddies, I need to calculate "covariance matrix" of the given joint PDF function. Joint PDF is fx(x1,x2,x3)=2/3(x1+x2+x3) over S (x1,x2,x3), 0<xi<1, i=1,2,3 How can I calculte the Covariance Matrix? Thanks

if you've got c1=2x+3x, and c2=x-y, with cov matrix x,y = [7 4].how do you find C = (c1,c2)transpose?

Homework Statement Let the random variables X and Y have the joint p.m.f.: f(x,y) = (x+y)/32 x=1,2, y=1,2,3,4. find the means \mux and \muy, the variances \sigma2x and \sigma2y, and the correlation coefficient \rho. Homework Equations \rho=(COV(X,Y))/\sigmax\sigmay The Attempt...

1. Let N and T be the number of users logged on and the time until the next log-off. The joint probability of N and T is given by P(N=η, X≤t) = (1-ρ)ρ^{η-1}(1-e^{-ηλt}) for η=1,2,...;t>0.) Find the correlation and covariance of N and T. 2. COV(X,Y) = E[XY]-E[X]E[Y] ρ_{X,Y} =...

Very sorry that I've double posted but I realized i placed the original post in Precalculus. 1. Homework Statement Question Let X and Y be independent random variables with variances 9 and 7 respectively and let Z = X - Y a) What is the value of Cov(X,Z) b) What is the value of...

This is probably a stupid question, but here goes: based on the covariance function of some (centered, stationary) Gaussian process - how can one determine non-degeneracy (here I mean for any choice of a finite number of sampling times, the resulting RV is AC). Ideas?

I was reading Turk and Pentland paper 'Eigenfaces for recognition' and they assert that, if M < N, the maximum rank of a covariance matrix is M - 1, being M the number of samples and NxN the size of the covariance matrix. Is there any simple demonstration of this fact? Thanks in advance...

Dear all, I was wondering how one in reality produces the so called "Covariance ellipse"? Lets say I have a set of data points with their error and fit a function to that data using 2 parameters just for simplicity. Now, I know that the covariance ellipse is an ellipse of equal...

Hi there, Can I ask (i) Is Lorentz covariance the same thing as Lorentz invariance? They seem to appear everywhere whenever we talk about space-time coordinates... what is the difference? (ii) Is an open string the same as a bosonic string? Do bosons only appear as open strings or as...

Homework Statement Let X be the number of 1's and Y be the number of 2's that occur in n rolls of a fair die. Find Cov(X, Y) Homework Equations Cov(X,Y) = E(XY) - E(X)E(Y) The Attempt at a Solution Both X and Y are binomial with parameters n and 1/6. Thus it is easy to find E(X)...

1. A (presumably) simple question: We are used to think that the affine connections emerge whenever one wants to differentiate a vector (tensor, spinor) on a curved manifold in general relativity. Now suppose that we are still on a flat background of special relativity, though in a...

Hi all, I have a stats problem I'm trying to figure out. Suppose I have a very large population (~millions) of colored balls with exactly 50% red, 30% green, 20% blue. If I take a random sample of 1000 of these balls, the distribution of colors I end up with can be modeled as a multivariate...

Im writing some java code and need help with some matrix math... :confused: Basically I am trying to figure out how to rotate an ellipse given the std deviations, means, and covariance matrix such that the major and minor axes are along the direction that has the greatest variance. This is just...

Hi friends, long time ago I noticed the following interesting similarity between classical mechanics and relativity. Consider particle moving in an external field and the action defined as a function of actual time t and position q: S(t,q) = \int_0^t L(q^r,\dot q^r,t´)dt´ The motion q^r is...

Homework Statement Suppose X1 , X2 , X3 , and X4 are independent with a common mean 1 and common variance 2. Compute Cov( X1 + X2 , X2 + X3). Homework Equations Cov (X,Y) = E[(X-u)(Y-v)] = E[XY] - uv, where u and v are the means of X and Y E[XY] = E[X]E[Y] E[X+Y] = E[X] + E[Y] The Attempt...