explain the covariance formula to a retard.
we have COV(X, Y) = E[ (X - E[X]) (Y - E[Y]) ]
i get why this works, but if we develop, we have :
COV = E[ X.Y + E[X].E[Y] - X.E[Y] - Y.E[X] ]
and this is where i'm confused, isn't E[ X.E[Y] ] = E[X].E[Y] ?
this doesn't makes sense as we would obtain :
COV = E[ X.Y - E[X].E[Y] ]
which is clearly wrong. what am i missing?
we have COV(X, Y) = E[ (X - E[X]) (Y - E[Y]) ]
i get why this works, but if we develop, we have :
COV = E[ X.Y + E[X].E[Y] - X.E[Y] - Y.E[X] ]
and this is where i'm confused, isn't E[ X.E[Y] ] = E[X].E[Y] ?
this doesn't makes sense as we would obtain :
COV = E[ X.Y - E[X].E[Y] ]
which is clearly wrong. what am i missing?