Covariance Definition and 161 Threads

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...

What is general covariance? See a very informative discussion at: https://www.physicsforums.com/showthread.php?t=197220&highlight=general+covariance"

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 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...

Is there a possibility that general covariance be an approximation or violated ?

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...