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

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Basic Math

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, andf(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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