Suppose X, Y, and Z are random variables with the 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 ≤ 0.875 , Y ≤ 1.125). (Round answer to five decimal places). (c) Find P(X ≤ 0.875 , Y ≤ 1.125 , Z ≤ 1). (Round answer to six decimal places).

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