In the sequel (XoX) denotes a (k+1)-dimensional normally distributed random vector. a) Assume that (X... X)...

  

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In the sequel (XoX) denotes a (k+1)-dimensional normally distributed random vector. a) Assume that (X... X) is independent, and put / :- (ie (1....,k): o(X) > 0). Show that E(Xol (XXx)) = Cov(Xo, X)/(X) (X - E(X)) + E(X). 167 Hint: Exercise 10.2. b) Determine E(Xol (X X)) without any further assumption on (X...X). c) Consider a one-dimensional Brownian motion (Y)re, Determine E(Y,Z) for t2 0, where Z=Y or Z:= Y, ds. In the sequel (XoX) denotes a (k+1)-dimensional normally distributed random vector. a) Assume that (X... X) is independent, and put / :- (ie (1....,k): o(X) > 0). Show that E(Xol (XXx)) = Cov(Xo, X)/(X) (X - E(X)) + E(X). 167 Hint: Exercise 10.2. b) Determine E(Xol (X X)) without any further assumption on (X...X). c) Consider a one-dimensional Brownian motion (Y)re, Determine E(Y,Z) for t2 0, where Z=Y or Z:= Y, ds.