Cov(Xi,Xj) = E((Xi-Mi)(Xj-Mj))
Is the above equivalent to:
I don't understand why the expectancy of (Xi-Mi)(Xj-Mj) would be different than just (Xi-Mi)(Xj-Mj)
Let's say I have two sets of data:
Set 1: 1,2,3 avg: 2
Set 2: 4,5 avg: 4.5
Is the following a covariance matrix?
(1-2)*(4-4.5) , (2-2)*(4-4.5) , (3-2)*(4-4.5) (1-2)*(5-4.5) , (2-2)*(5-4.5) , (3-2)*(5-5.5)
I'm reading online and it seems like a covariance matrix composed of two data sets should be a 2x2 matrix, but in this case, I have a 2x3 matrix. How do I go from what I have to the correct 2x2 matrix?