The joint density function for random variables X, Y, and Z is f(x, y, z) = Cxyz if 0 <= x <= 2, 0 <= y <= 1, and 0 <= z <= 2, and f(x, y, z) = 0 otherwise.  (a) Find the value of the constant C.  (b) Find P(X <= 1, Y <= 1, Z <= 1).

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