Exercise 5 Write a program that will sample from a standard Brownian motion using step size...

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Exercise 5 Write a program that will sample from a standard Brownian motion using step size At = 1/400. Make a graph of Bt, 0 t 3 from your simulation for one trial. Repeat the simulation 1000 times to give estimates for the following: P{ max Bt > 1}, 0 0, B3 > 0}. Find the exact values of these probabilities and compare your simulations with the exact values. You may use any computer language and/or package that you choose. Exercise 5 Write a program that will sample from a standard Brownian motion using step size At = 1/400. Make a graph of Bt, 0 t 3 from your simulation for one trial. Repeat the simulation 1000 times to give estimates for the following: P{ max Bt > 1}, 0 0, B3 > 0}. Find the exact values of these probabilities and compare your simulations with the exact values. You may use any computer language and/or package that you choose.