Let X t describe a Brownian particle with parameter = 4 starting at X = 0

Let X_t describe a Brownian particle with parameter σ = 4 starting at X = 0 when t = 0 and moving for a time t = T /4. Now let Y_s, for s = 0 to s = 3T /4, describe the motion of the same particle from time T/4 until time T. How is X_T/4 distributed? How is Y_3T/4 distributed? How is X_T/4 + Y_3T/4 distributed? Work this out either analytically or via simulation, for T = 12. This problem illustrates the inifinite divisibility property of the Wiener process.