Question: 4. The joint probability density function of random variables X, Y , and Z is given by f (x, y, z) = B c(x +

4. The joint probability density function of random variables X, Y , and Z is given by f (x, y, z) = B c(x + y + 2z) if 0 ≤ x, y, z ≤ 1 0 otherwise.

(a) Determine the value of

c.

(b) Find P (X < 1/3 | Y < 1/2, Z < 1/4).

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