6. Consider the 3-period binomial model for the stock price process { Sn }on

6. Consider the 3-period binomial model for the stock price process on (03, F, P), with probability of an up move P(U) p and with up and d 2 and down factors u - respectively. Fix So 2 and define Mn max{S0, ST, ... , Sn} as the sampled maximum of the stock price at times n 0, 1, 2, 3. (a) Determine the support (range) of each random variable MI M2 and 1113. (b) Determine the probability distribution (p.m.f.) of M3. (c) Determine the conditional expectations: (i) E M2 1 a(S1)]; (ii) E[M3 1 a(S1)]