4. Suppose that in the target zone between the Hong Kong and the US dollars the log price of the USD in HKD is given by: 2 = gxt + gEtStH, where x; = m; mj. Also suppose that z; can be described as a discrete random variable. It can take on the values 1 or 3, each with probability 0.5, and is independently distributed over time. (a) Find the two possible values of s;. (b) Find the variance of z; and the variance of s;. (c) If UIP holds, find the two possible values of the international interest rate differential, iy i;. Also find the value of the log forward exchange rate f