Write the formula for covariance between X and Y

Write the formula for Pearson correlation coefficient

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

What is the formula for calculating the mutual information between two discrete random variables X and Y?

I(X;Y) = ∑∑ P(x,y) log(P(x,y)/(P(x)P(y)))

Write the formula for Mahalanobis distance

D^2 = (x - μ)^T Σ^(-1) (x - μ)

Mutual information I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X)

Mutual information measures dependence between variables X and Y

Write the equation for cross-entropy loss

H(y, p) = -Σ(y_i * log(p_i)) for all i

Write the formula for normal distribution PDF

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