In the actual problem, we often want to use the existing data to determine whether the occurrence of two events is related. Of course, an angle to find the intrinsic logic of the two events, this angle needs to delve into the nature of the two events, and another angle is the simple method offered by probability theory: based on the probability of two events, we can describe the correlation of two random variables.
In fact, we can understand the covariance to a certain extent the correlation of two random variables in the back of the formula, the perceptual, E[xy] is an actual x, Y simultaneous events, and E[x]e[y] is we give a comparison of a "hypothetical X, y independent" model, Comparing the difference between the actual situation and the ideal condition, it is obvious that the difference is smaller, which shows that the closer the actual situation is to the hypothetical model, the smaller the correlation of X and Y.
The covariance has the following computational properties:
(1), (2), (3) The combination of definitions, comparative good certificate, it is no longer here, the main discussion (4) of the proof method.
"A first Course in probability"-chaper7-combinatorial analysis-expected properties-covariance, correlation coefficients