Question

Covariance of Random Variables x and y

- Give Equation
- What values can Covariance take?
- Why is covariance not preferred when looking at relationships between two variables?

Answer 1

The covariance of random variables x and y can be positive, negative, or zero. Covariance is not preferred when looking at relationships between two variables because it does not provide a standardized measurement like correlation does.

Step-by-step explanation:

The covariance of random variables x and y can be calculated using the following equation:

cov(x, y) = E[(x - E[x])(y - E[y])]

The values that covariance can take are not limited, as it can be positive, negative, or zero. A positive covariance indicates a positive relationship between x and y, while a negative covariance indicates a negative relationship. A covariance of zero means there is no linear relationship between x and y.

Covariance is not preferred when looking at relationships between two variables because it does not provide a standardized measurement like correlation does. Covariance values are affected by the scale of the variables, making it difficult to compare the strength of the relationships between different pairs of variables.