# begin align a_ 00 a_ 00 a_ 10 a_ 20 a_ 30 a_ 00 a_ 01 a_ 02 a_ 03 sum_

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 \begin{align} f(0,0) = p(0,0) = a_{00} \\ f(1,0) = p(1,0) = a_{00} + a_{10} + a_{20} + a_{30} \\ f(0,1) = p(0,1) = a_{00} + a_{01} + a_{02} + a_{03} \\ f(1,1) = p(1,1) = \sum_{i=0}^{3} \sum_{j=0}^{3} a_{ij} \\ \end{align} \begin{align} f_x(0,0) = p_x(0,0) = a_{10} \\ f_x(1,0) = p_x(1,0) = a_{10} + 2a_{20} + 3a_{30} \\ f_x(0,1) = p_x(0,1) = a_{10} + a_{11} + a_{12} + a_{13} \\ f_x(1,1) = p_x(1,1) = \sum_{i=1}^{3} \sum_{j=0}^{3} a_{ij} i \\ f_y(0,0) = p_y(0,0) = a_{01} \\ f_y(1,0) = p_y(1,0) = a_{01} + a_{11} + a_{21} + a_{31} \\ f_y(0,1) = p_y(0,1) = a_{01} + 2a_{02} + 3a_{03} \\ f_y(1,1) = p_y(1,1) = \sum_{i=0}^{3} \sum_{j=1}^{3} a_{ij} j \\ \end{align} \begin{align} f_{xy}(0,0) = p_{xy}(0,0) = a_{11} \\ f_{xy}(1,0) = p_{xy}(1,0) = a_{11} + 2a_{21} + 3a_{31} \\ f_{xy}(0,1) = p_{xy}(0,1) = a_{11} + 2a_{12} + 3a_{13} \\ f_{xy}(1,1) = p_{xy}(1,1) = \sum_{i=1}^{3} \sum_{j=1}^{3} a_{ij} i j \\ \end{align}