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Suppose X, Y, and Z are random variables with joint density function f(x, y, z) = Ce-(0.5x+0.2y+0.1z) if x 0, y 0, z 0, and f(x, y, z) = 0 otherwise.
(a) Find the value of the constant C.
(b) Find P(X 1, Y 1).
(c) Find P(X 1, Y 1, Z 1).
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