Write the formula for normal distribution PDF

Write the equation for sigmoid function σ(x) = 1/(1+e^-x)

σ(x) = 1 / (1 + e^-x)

Write the formula for Pearson correlation coefficient

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

What the characteristic function φ(t) = E[e^(itX)] does: Fourier transform of the PDF

Characteristic function φ(t) = E[e^(itX)] represents the Fourier transform of the probability density function (PDF)

Write the formula for Mahalanobis distance

D^2 = (x - μ)^T Σ^(-1) (x - μ)

What Chebyshev's inequality says: P(|X-μ| ≥ kσ) ≤ 1/k²

Chebyshev's inequality states that the probability of a random variable deviating from its mean by at least k standard deviations is less than or equal to 1/k²

Write the formula for covariance between X and Y

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