Practically, $P_{Π = π} ( X , Y )$ is only known through a finite sample $S_{Π = π} ( X , Y ) = \{( x_1 , y_1 ), ( x_2 , y_2 ), ⋯ , ( x_n , y_n )\}$ (a scatter plot ). Hence, we have a double random process:

1. Draw Pair $(P_{Π = π} ( X , Y ), G=g)$ from mother distribution $P_M(P_{Π = π} ( X , Y ),G)$.
2. Draw $n$ samples from $P_{Π = π} ( X , Y )$: $S_{Π = π} ( X , Y ) = \{( x_1 , y_1 ), ( x_2 , y_2 ), ⋯ , ( x_n , y_n )\}$
3. Repeat the process to obtain emough training and/or test examples: $\{ (S_1(X,Y),g_1), (S_2(X,Y),g_2), \cdots, (S_N(X,Y),g_N) \}$