Consider the geometric SDE: dSt = Stdt + StdWt where St is assumed to represent an equity

Question:

Consider the geometric SDE:
dSt = μStdt + σStdWt
where St is assumed to represent an equity index. The current value of the index is
S0 = 940
It is known that the annual percentage volatility is 0.15. The risk-free interest rate is constant at 5%. Also, as is the case in practice, the effect of dividends is eliminated in calculating this index. Your interest is confined to an eightday period. You do not see any harm in dividing this horizon into four consecutive two-day intervals denoted by Δ.
(a) Use coin tossing to generate random errors that will approximate the term dWt, with
H = +1
T = −1
(b) How can you make sure that the limiting mean and variance of the random process generated by coin tossing matches that of dWt, as Δ → 0?
(c) Generate three approximate random paths for St over this 8-day period.