1.5. Implement the Euler code of Example 1.6. Plot numerical solutions for = 1 and ...

1.5. Implement the Euler code of Example 1.6. Plot numerical solutions for α = 1 and

β = 2 over 0 ≤ t ≤ 1 . Now generate simultaneously m = 300 realizations of the solution of the SDE (for α = 1 and β = 2) and draw a histogram of their values at time t = 1 , say, using bins of width 0.25 from 0 to 5 ; see that almost all solutions have a smallish numerical value (less than one). Nonetheless, compute the mean of the values at time t = 1 and see that it is roughly e1 = 2.718 !