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(20 points) Let Xi, i = 1, 2 be independent random variables that have the following distri- butions: X; = 1 with probability p and X, = -1 with probability 1 - p: p Xi 1 - P -1 Define B1 = X1 B2 = X1+ X2 Denote an upward move of X; by G and a downward move by B. Consider the following sample space 2 = {GG, GB, BG, BB} Let Fi, i = 1,2 be the natural filtration associated with the process Bi. (a) (10 points) Find Fi and F2.(b) {10 points) Describe 21 = E[Bg|}'1] as a map from (2 into the set of real numbers 1R. Find the probability p such that the process {Bk 3;} is a martingale