I have two objects A & B.

Two functions f(u,v) & g(u,v), where u & v are rotational angles along axis
of the objects. The functions return x, y coordinates relative to a center
point.  u, v, x, and y are treated as discreet.

Distributions are formed corresponding to the number of times a coordinate
is hit.  For example, for 16 distinct combinations of u and v, the
corresponding distributions may be:

Object A, function f

1 2 1                1 hit to coordinate (-1, -1); 2 hits to coordinate
(0, -1);
2 4 2                4 hits to coordinate (0, 0), etc.
1 2 1

Object A, function g

1 2 3
1 3 3
0 1 2

Object B, function f

1 2 1
2 3 1
3 2 1

Object B, function g

2 2 0
2 4 2
0 2 2

I need to show the dependence or independence of these distributions. In
particular: 1) for a given object, are functions f and g independent; 2) for
a given function, is it independent of the object.

Do I have enough information to do any sort of meaningful analysis? How do I
go about solving this?

The actual distributions are larger with many more combinations of u and v.




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