Definition of Covariance

Covariance measures the statistical relationship between two random variables. It quantifies how the variables change together, providing insight into the directional relationship between them.

Key Points:

• Covariance is a measure of the joint variability of two random variables.
• A positive covariance indicates that the variables tend to move in the same direction.
• A negative covariance indicates that the variables tend to move in opposite directions.
• A covariance close to zero suggests little to no linear relationship between the variables.
• Covariance is affected by the scale of the variables, making it difficult to interpret on its own.

Mathematical Definition:

The covariance between two random variables X and Y is calculated using the following formula:

Cov(X, Y) = E[(X - μX)(Y - μY)]

Where:

• Cov(X, Y) is the covariance between X and Y
• E[] denotes the expected value
• X – μX represents the deviation of X from its expected value
• Y – μY represents the deviation of Y from its expected value