15.12 Suppose we observe the trajectory of a particle at time t = 1 and we see that the position is Xt = 4. We need to estimate the distribution of the particle at time s = 1/2. To do this, we assume that the position at time t is given by a standard Brownian motion. Calculate the distribution of the position at time s = 1/2 given that at time t = 1 it was at Xt = 4 and we know that at time 0 the position was at X0 = 0. How does this distribution change if we know that at time 0 the position of the particle was at X0 = 3?