gen-in-3-4-sentences-explain-variance-and-covariance-state-any-k-7024

In 3-4 sentences, explain variance and covariance. State any key formula.

# Variance and Covariance **Variance** measures how much a single variable spreads out from its mean, calculated as the average of squared deviations: **Var(X) = E[(X - μ)²]** or equivalently **σ² = Σ(xᵢ - μ)²/n**. **Covariance** measures how two variables vary together, indicating whether they tend to increase or decrease in tandem: **Cov(X,Y) = E[(X - μₓ)(Y - μᵧ)]**. A positive covariance means the variables tend to move in the same direction, while negative covariance indicates they move in opposite directions. Note that variance is simply the covariance of a variable with itself: Var(X) = Cov(X,X).