The joint density function for random variables X, Y, and Z is f(x, y, z)= Cxyz if 0≤x≤1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2, and f(x, y, z) =

Question

The joint density function for random variables X, Y, and Z is f(x, y, z)= Cxyz if 0≤x≤1, 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).

Kunduz · Accepted Answer

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