The probability of an event ranges between impossible and certain. Where X is the set of all possible events x, . The probability that some possible event or other occurs is certain. Sometimes we want to look at continuous probability densities rather than just discrete distributions. If random variables are independent, then their covariance is zero.
Covariance ranges over the real numbers.
Thus the correlation coefficient always has the same sign as covariance. Correlation coefficient often written as r . Like covariance, it measures the linear association between two variables. If is high, then it is possible to make good predictions about one variable if you know the other. Non-linear associations not picked up by r .