You are given the prior distribution P(X), and two conditional distributions P (Y |X) and P (Z|Y) as below (you are also given the fact that Z is independent from X given Y). All variables are binary variables. Compute the table of their joint distribution based on the chain rule. Your might round your answers to 4 decimal places. (4 Points) X P(X)
0 0.1
1 0.9
Y X P(Y|X)
0 0 0.600
1 0 0.400
0 1 0.500
1 1 0.500
Z Y P(Z|Y)
0 0 0.400
1 0 0.600
0 1 0.800
1 1 0.200
X Y P(X, Y)
0 0
1 0
0 1
1 1
X Y Z P(X, Y,Z)
0 0 0
1 0 0 0.18
0 1 0 0.032
1 1 0
0 0 1 0.036
1 0 1
0 1 1 0.008
1 1 1