Problem 3 [13 points] Consider a 2-step trinomial non-recombining lattice tree model. For each step, there are three possibilities for the stock price: an up movement (u), a down movement (d) or no movement (n). (a) Write down the set or sample space, , containing all possible outcomes for this 2 -step trinomial tree. If we consider the collection of all subsets of , how many subsets are there in this collection? [ 2 point] (b) Suppose the respective probabilities of events {u} and {d} are 3/7 and 2/7. Define or construct the probability measure for each individual element . [3 points] (c) Write down the -algebra or -field {l} keeping track the outcomes for each time step i= 0,1,2. [3 points] (d) Consider the given in (a). Under the trinomial asset pricing model suppose S0=50,d= 10/11 and u=12/11; clearly, {Si} is a stochastic process, i.e., Si 's are random variables for i=0, 1,2 . Find Sl(), i.e., what is the function Sl() ? [3 pts] (e) Consider the interval B=[2e1,2e+1]. What is Sll(B) ? Recall that Sl is a random variable and by definition it maps into . [2 pts]