Given the random variable (X, Y, Z) with density function kxyz if (x,y,z) EC fx,y,z(x, y, z) = 0 rest where C= {(x, y, z

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Given The Random Variable X Y Z With Density Function Kxyz If X Y Z Ec Fx Y Z X Y Z 0 Rest Where C X Y Z 1 (57.62 KiB) Viewed 80 times

Given the random variable (X, Y, Z) with density function kxyz if (x,y,z) EC fx,y,z(x, y, z) = 0 rest where C= {(x, y, z): 0 5 x 51,05 y 52,05z S 3}. a) Calculate the value of k, such that fX, Y, Z (X, Y, Z) is a function of density. b) Calculate P (X</2, Y> 12, 1<Z<2). c) Calculate the marginal density functions of (X, Y), (Y,Z). d) Calculate the marginal density function of the random variable (X, Y) conditioned by the variable Z