LetW(t) be a standard Brownian motion.

(a) Calculate the probabilityP(W(1) +W(2)>2).

(b) Show that the time-inverted processW1(t) =tW(1) is also a standard Brow-

nian motion.

(c) The stochastic process

W(t),ifW(t)0;W2(t) =|W(t)|=W(t),ifW(t)<0

is called Brownian motion reflected at the origin. Calculate the mean and variance ofW2(t).