Kovariansse

Kovariansse is a statistical measure that describes the extent to which two random variables change together. A positive covariance indicates that the two variables tend to increase or decrease in tandem. For example, if ice cream sales and temperature are positively correlated, as temperature rises, ice cream sales also tend to rise. A negative covariance suggests that as one variable increases, the other tends to decrease. For instance, if hours spent studying and hours spent playing video games are negatively correlated, as study hours increase, video game hours might decrease.

A covariance of zero implies that there is no linear relationship between the two variables, meaning they do not tend to move in a predictable way with respect to each other in a linear fashion. The magnitude of the covariance is sensitive to the scale of the variables involved. A large positive or negative covariance does not necessarily mean a strong relationship if the variables themselves have large scales. To address this, a standardized version called the correlation coefficient is often used, which ranges from -1 to +1 and is independent of the scale of the variables. Covariance is fundamental in portfolio theory, where it is used to measure the risk of a portfolio by understanding how the returns of different assets move together. It is also a key component in calculating the variance of a sum of random variables.