Question: The joint density function for random variables X, Y, and Z is f (x, y, z) = Cxyz if 0 < x < 2, 0

The joint density function for random variables X, Y, and Z is f (x, y, z) = Cxyz if 0 < x < 2, 0 < y < 2, 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).
(c) Find P(X + Y + Z < 1).

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