4. Suppose (2, B, P) is the uniform probability space; that is, ([0, 1], B, λ) where A is the uniform probability distribution. Define X(w) = w. (a) Does there exist a bounded random variable that is both independent of X and not constant almost surely? (b) Define Y = X(1 - X). Construct a random variable Z which is not almost surely constant and such that Z and Y are independent.

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