GATE Stochastic Processes: Brownian Motion – Previous Year Questions

6 GATE previous year questions on Brownian Motion (Stochastic Processes, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q12 (1 mark, Multiple choice) – For standard Brownian motion W(t),find Var[W(1)W(2)].
2. GATE 2022 ST Q24 (1 mark, Numerical answer) – B(t) is standard Brownian motion. If P[B(2)+2B(3)>1]=1−Φ(1/√α),α>0,find α as an integer.
3. GATE 2023 ST Q33 (1 mark, Numerical answer) – For standard Brownian motion W t,find E(W₄² W₂=2),as an integer.
4. GATE 2024 ST Q22 (1 mark, Multiple choice) – For standard Brownian motion W, which is not true?
5. GATE 2025 ST Q31 (1 mark, Numerical answer) – For standard Brownian motion W, find E[(W(2)+W(3))²] (integer).
6. GATE 2026 ST Q31 (1 mark, Numerical answer) – For standard Brownian motion W, let Z₁=W(1)+W(2),Z₂=W(2)+W(3). If ρ is their correlation, find 10ρ to two decimals.