Question: Exercise 3: Let {B,, t 2 0 } be a standard Brownian motion. Let 0 Exercise 3: Let {Bt, t 0 ) be a standard

Exercise 3: Let {Bt, t 0 ) be a standard Brownian motion.

Exercise 3: Let {B,, t 2 0 } be a standard Brownian motion. Let 0

Exercise 3: Let {Bt, t 0 ) be a standard Brownian motion. Let O s < t and a, b e R. (a) Calculate E(aBs + bBt). (b) Show that Var(aBs + bBt) = (a + s + b2(t s). (c) What is the distribution of aBs + bBt. (d) Calculate the probability P(5B3 - 3B2 1).

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