4. Given Xj = 1 Wj = H -1 wj =T is a random variable with P(Xj = 1) = P(Xj = -1) = ?, we define the symmetric random walk as k MK = EXj j=1 With the symmetric scaled random walk given by w ( n ) ( t ) = - 1 Vn Mnt Consider our binomial model with U = - and D = -. For a given path, let Hot be the number of "heads" or "ups" and Int be the number of "tails" or "downs". (a) Write number of flips nt in terms of Hnt and Int (b) Write the position Mnt in terms of Hnt and Int (c) Before we had an expression like S(T) = S(0) (1 + U)"(1+ D) N-k. Write a similar expression in terms of S(0), o, n, t and Mnt