A Gaussian Process (GP) is a distribution over functions: any finite collection of function values follows a multivariate Gaussian distribution. The GP is fully specified by a mean function m(x) and a covariance (kernel) function k(x, x'). Here we use the squared-exponential kernel k(x,x') = σ² exp(−|x−x'|²/2ℓ²), where ℓ is the length scale controlling smoothness. When observations are added, the GP posterior is computed via exact Bayesian updating: the posterior mean and variance have closed-form solutions involving the kernel matrix K. The shaded region shows ±2σ of the posterior uncertainty — notice how it collapses near observations and expands in unexplored regions.