Let Xi , i = 1, 2 be independent random variables that have the following distributions: Xi = 1 with probability p and Xi = 1 with probability 1 p: Define B1 = X1, B2 = X1 + X2

Denote an upward move of Xi by G and a downward move by B.

Consider the following sample space = {GG, GB, BG, BB}

Let Fi , i = 1, 2 be the natural filtration associated with the process Bi .

Find F1 and F2.