An asymmetric (biased) random walk moves right with probability p and left with q=1−p. The drift velocity is v = p−q = 2p−1 and diffusion coefficient D = 4pq. The Fokker-Planck equation gives P(x,t) = Gaussian with mean ⟨x⟩ = vt and variance σ² = 2Dt. First-passage times exhibit exponential tails when drifted away from a boundary.