Let X be a standard Brownian motion, and let Y1 and Y2 satisfy the following system of SDEs: dY1 (t) = ali(t)dt - Y2(t)dX(t), Y1(0) = y10 dY2(t) = alz(t)dt + Yi(t)dX(t), Y2(0) = 120, where y10. )20 are given constants.. (a) Show that the sum of the squares process S(t) = Y2(t) + Y2(t) is deterministic. For which values of a does S become a constant? (b) Calculate E[Y1 (t)] and cov(Y1 (t), Y2(t))