"A first Course in probability"-chaper7-expected nature-correlation coefficient

As we've described before, covariance can describe the correlation between two variables to some extent, but sometimes it's not as accurate as the following example:

Essentially the same two random variables, the independence is constant, but through this equation I see that if a constant is added to the front of a random variable, the result of the covariance is a relatively large gap, so it is not good for us to measure the independence between the two random variables, So here we standardize the definition of variables that describe correlations, which introduces the correlation coefficients:

We can deduce the importance of correlation coefficients:

"A first Course in probability"-chaper7-expected nature-correlation coefficient