Suppose X, Y, and Z are random variables with joint density function f (x, y, z) =

Question:

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).