# Question

Given the joint probability distribution

f(x,y,z) = xyz/108 for x = 1,2,3; y = 1,2,3; z = 1,2

Find

(a) The joint marginal distribution of X and Y;

(b) The joint marginal distribution of X and Z;

(c) The marginal distribution of X;

(d) The conditional distribution of Z given X = 1 and Y = 2;

(e) The joint conditional distribution of Y and Z given X = 3.

f(x,y,z) = xyz/108 for x = 1,2,3; y = 1,2,3; z = 1,2

Find

(a) The joint marginal distribution of X and Y;

(b) The joint marginal distribution of X and Z;

(c) The marginal distribution of X;

(d) The conditional distribution of Z given X = 1 and Y = 2;

(e) The joint conditional distribution of Y and Z given X = 3.

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