Question: 3.60 The joint probability density function of the random variables X, Y , and Z is f(x, y, z) = 49 xyz2 , 0 <

3.60 The joint probability density function of the random variables X, Y , and Z is f(x, y, z) =

49 xyz2 , 0 < x,y < 1, 0 < z < 3, 0, elsewhere.

Find

(a) the joint marginal density function of X and Y ;

(b) the marginal density of Z;

(c) P(14

< X < 12

, Y > 13

, 2 < Z < 3);

(d) P(0 < Z < 2 | X = 12

, Y = 12

).

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