Write the formula for Mahalanobis distance

Write the formula for covariance between X and Y

Cov(X, Y) = Σ((Xi - X̄)(Yi - Ȳ)) / (n - 1)

Write the formula for normal distribution PDF

Normal distribution PDF: 𝑋/(σ√2π) * e^(-(X-μ)^2/(2σ^2))

Write the formula for Pearson correlation coefficient

r = Σ((xi - x̄)(yi - ȳ)) / (√Σ(xi - x̄)² * √Σ(yi - ȳ)²)

Why the L1 unit ball is a diamond shape and the L2 unit ball is a circle

L1 norm: Manhattan distance, L2 norm: Euclidean distance

Why L1 distance is called Manhattan distance — grid-like paths

L1 distance mimics grid-like city blocks, hence "Manhattan" distance

Write the formula for KL divergence D_KL(P||Q)

D_KL(P||Q) = Σ P(x) log(P(x)/Q(x)) for all x in the support of P