7* Consider the probability space (2, H, P) where 2 is the interval [0, 1), H is the Borel o-algebra on [0, 1) and P is the Lebesgue measure (on [0, 1)). Every w E [0, 1) has a unique binary expansion containing an infinite number of zeros, e.g. 47 64 = .101111000000 .. . . Now, for any w E [0, 1) write down the expansion w = .W1w2 . .., and define Xn(W) = Wn. (a) Draw the graphs of X1, X2, and X3. (b) Verify that X1, X2, . .. are Ber(1/2) distributed random variables