Cov(X, Y ) = E[XY ] − E[X]E[Y ]

The equation you provided is the formula for covariance, a measure of how much two random variables vary together. Here's a step-by-step explanation:

1. Cov(X, Y): This represents the covariance between two random variables X and Y. Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated.

2. E[XY]: This is the expected value (or the mean) of the product of X and Y. In other words, it's the average value you would get if you multiplied X and Y together for all data points.

3. E[X] and E[Y]: These are the expected values (or the means) of X and Y, respectively. It's the average value of X and Y.

4. E[XY] - E[X]E[Y]: This is the formula for covariance. It's the difference between the expected value of the product of X and Y and the product of the expected values of X and Y. If this value is positive, X and Y tend to move in the same direction (i.e., when X increases, Y also increases, and vice versa). If this value is negative, X and Y tend to move in opposite directions (i.e., when X increases, Y decreases, and vice versa). If the value is zero, there is no linear relationship between X and Y.