1. Let (2., F, P) be the probability triple, where 2. is the set of all infinite sequence of coin tosses. Recall the definition of the stock price at time t = 2 in the binomial model sou ? : W1 = W 2 = H , S2 ( W ) = soud : W1 / W2 , sodz : W1 = W2 = T. Recall also that the o-algebra Fi generated by the first coin toss is F1 = {0, 0, AH, AT } , where AH = { w E fool w = WI W2..., W1 = H}, AT = {W E fool w = w, w2..., W1 = T}, (1) a. Is S2 a R. V. with respect to F1. In other words, does for every BE B(R), the set {w/ S2(W) E B } E F1? b. (Bonus) What is the smallest o-algebra F, such that S2 a R.V. with respect to F