What is Covariance: Definition and 171 Discussions
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret because it is not normalized and hence depends on the magnitudes of the variables. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation.
A distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which in addition to serving as a descriptor of the sample, also serves as an estimated value of the population parameter.
Hi, what is the difference between Lorentz Invariance and Lorentz Covariance?
From my lecture note (Group theory course) Invariance and Covariance where defined as follows:
Invariance: refers to the property of objects being left unchanged by symmetry operations.
Covariance: refers to...
Homework Statement
Find E(XY), Cov(X,Y) and correlation(X,Y) for the random variables X, Y whose joint distribution is given by the following table.
X
1 2 3
Y -1| 0 .1 .1
0| 0 .5 .6
1| .2 0 0The Attempt at a...
Hi All,
I have a data set consisting of (x,y,z) coordinates. I can calculate the covariance between them just fine. Calculating all the covariances between the three variables gives me a nice 3x3 matrix. However, the points have a weighting value as well. I don't know how to account for the...
Hi,
While teaching myself Time Series Analysis and ARMA processes in particular, I came across the question, whether two ARMA(p,q) processes
\varphi(B)X_t=\theta(B)Z_t \qquad\qquad \tilde \varphi(B)\tilde X_t=\tilde \theta(B)\tilde Z_t\
with different autoregressive and/or moving average...
Can someone help me out with this idea?
Let's say we have a diffeomorphism. We know that under certain circumstances (invariance of the metric) this diffeomorphism is an isometry. Here is the part I'm not sure about. Is an isometry always just a statement about the principle of covariance...
Dear all,
I'm trying to implement an Extended Kalman Filter for position, velocity and orientation tracking of a rigid body and I am using quaternions for representing the orientation in the state vector. As this is the first time I have to work with a Kalman Filter, and the project is on a...
What are the transformation laws of covariant and contravariant tensors? Also, how do I deal with mixed tensors in terms of transformations and in representation?
Hello
I had measured luminescence decay profile. Then I want to fit a function which would approximate my experimental date. For that I make a simple program in LabWiev. The problem is that, that program give me out a negative values in covariance matrix. Why that?
P.S.
Sorry for my English
Hello,
I have trying to understand this excercise for quite a time, but still with no results. So I thought maybe you can help me ;P
Here is the problem. I have a function given by:
x(t)=\sum_i A_i s(t-iT-\tau_i)+n(t)
where:
- \left\{A_i\right\}_{i\in Z} is a random point process...
Hey, I posted earlier about the tensor covariant derivative, and the help was great, that makes sense to me now.
However, I am getting really really stuck on the concept of covariant vectors vs. contravariant vectors. I've looked through as many resources as I can - wikipedia, mathworld, the...
Homework Statement
I have a joint pdf f_{XY}(x,y) = (2+x+y)/8
and I have to find cov(x,y)
Homework Equations
Now I know the formula is cov(X,Y)=E((X-mu)(Y-v)) where E(X)=mu and E(Y)=v
Well I found that formula on wikipedia, but it doesn't make sense to me because if E(X)=mu then...
According to the principle of general covariance, the form of equations should be independent of the coordinates chosen. In general relativity, this is implemented by expressing laws of physics as tensor equations.
In physics equations are often expressed in index notation, which allows...
Suppose X_1,...,X_n are independent and identically distributed random variables.
Now suppose I picked m_1 random variables from the set X_1,...,X_n and defined Y_1 as the sum of the m_1 variables, where m_1 is also a random variable.
Now suppose I did this again and I picked m_2 random...
Can someone explain to me what it means to be "covariant" in the context of special relativity and Lorentz transformations? I already checked wikipedia.
Hi. At the moment in class we are going over statistics :yuck:
Anyway, the formula I've been using for covariance between two sets of data is:
s_{xy} = \frac{1}{n}\sum\limits_{i = 1}^n {x_i y_i } - \overline x \overline y
Now, if i was to get a question such as:
"If all the...
I have 2 normally distributed dependent random variables, X and Y, and I have the mean and variance of both of them, and I want to find the covariance (or correlation) between X and Y.
Now the formula for the covariance is Cov(XY) = E(XY) - E(X)E(Y). So I tried to calculate E(XY) via the...
What is the definition of "general covariance"?
What is the definition of "general covariance"?
Is it sufficient for a theory to be written only in terms of tensors for it to be generally covariant? Is it necessary for a theory to be able to be written solely in terms of tensors for it to...
I do have a series of channels that contain the number of radioactive counts within a small energy range. Since the occurence of radioactive decay is statistical, the error in the number of counts is simply the square of the number of counts. Each channel contains counts from two different...
Greetings,
In some discussions about GR, I heard the term "covariance" and covariant form (eg, covariant form of Maxwell's equations) pop up often.
I've been wondering for a while why the notion of covariance in GR is so important. I have some background in mathematical physics, so I know...