15.6 Using your choice of software, simulate Bt a standard Brownian motion on the interval t ∈ [0, 2]. Using the simulated paths and the Central Limit Theorem, estimate E[B4 2], E[B8 2], E[B20 2 ].

Then simulate each of the processes B4 t , B8 t , B20 t separately and obtain the previous expectations at t = 2 that way as well.

Compare all the numbers obtained and also compare with the values in the previous problem. Use a minimum of 1 million simulated paths, and for each path use a time increment of Δt = 0.01.