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Exercise 5 Suppose we have a simple process of the following type. At = 1, Out 1/2, At = 0 B1/2 2 0 2 B1/2 0 Let Zt = As dB s 1. Find E[Z3/2] 2. Find E[Zi], E[Z?] 3. True or false: P{Z1 2 0} - 1/2. Give reason. 4. Does Z1 have a normal distribution? Give reason. 5. lim P{Zt > 0}. t->OCExercise 5 Suppose we have a simple process of the following type. At = 1, Out 1/2, At = 0 B1/2 2 0 2 B1/2 0 Let Zt = As dB s 1. Find E[Z3/2] 2. Find E[Zi], E[Z?] 3. True or false: P{Z1 2 0} - 1/2. Give reason. 4. Does Z1 have a normal distribution? Give reason. 5. lim P{Zt > 0}. t->OC