Let (W)to be a Brownian Motion. (a) Is (W) a martingale ? (If so, prove it. If not, explain why.) (b) Let X+= Wt. Is (X) a martingale ? (If so, prove it. If not, explain why.) (c) Letσ0 and μER. Also let Y₁ = exp(σW₁ + μt). Determine the condition on μ and σ that will make (Y) be a martingale. (d) Let ZterYt. Determine the condition on μ and σ that will make (Z+) be a martingale.