Title: Correlation Date: 2010-01-28 00:45 Author: Andrea Zonca Tags: physics Slug: correlation
Expectation value or first moment of a random variable is the probability weighted sum of the possible values (weighted mean).Expectation value of a 6-dice is 1+2+3+4+5+6 / 6 = 3.5
Covariance of 2 random variables is:
COV(X,Y)=E[(X-E(X))(Y-E(Y))]=E(X*Y) - E(X)E(Y)
i.e. the difference between the expected value of their product and the product of their expected values.
So if the variables change together, they will have a high covariance, if they are independent, their covariance is zero.
Variance is the covariance on the same variable, :
COV(X,X)=VAR(X)=E(X**2) - E(X)**2
Standard deviation is the square root of Variance
Correlation is:
COR(X,Y)=COV(X,Y)/STDEV(X)*STDEV(Y)
http://mathworld.wolfram.com/Covariance.html