#1
Consider two discrete variables x and y each having three possible states, for
example x, y ∈ { 0, 1, 2 } . Construct a joint distribution p(x, y) over these variables
having the property that the value  xi that maximizes the marginal p(x), along with
the value  yi that maximizes the marginal p(y), together have probability zero under
the joint distribution, so that p(  xi,  yi) = 0.
 
#3
y 0 1 2
x
0 0.0 0.2 0.3
1 0.2 0.0 0.0
2 0.3 0.0 0.0

this is one answer,i got it ,but i did it just by trial and error.how to formalize it with some algo


0.00 0.36 0.24
0.20 0.00 0.00
0.20 0.00 0.00
this is also another solution
 
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