A random walk starts at position x₀ > 0. The first passage time T to reach the boundary at 0 follows an inverse Gaussian (Wald) distribution: f(t) = x₀/√(2πt³) · exp(−x₀²/(2t)) for a driftless walk. Adding drift μ shifts the peak and changes the tail. The simulation (blue) converges to the theoretical curve (orange).