The, 3, moment about the mean of the r.v. number of 2-dim subcubes contained in the tr\ uth table of a random Boolean function is n 4 3 2 2 n (n - 1) (9 n + 6 n + 21 n - 16 n - 34) ---------------------------------------------- 32768 and in Maple notation 1/32768*2^n*n*(n-1)*(9*n^4+6*n^3+21*n^2-16*n-34) hence the scaled, 3, moment is 4 3 2 1/2 2 (9 n + 6 n + 21 n - 16 n - 34) 2 ----------------------------------------- n 3 1/2 2 (2 n (2 n + n - 3)) (2 n + 2 n + 3) and in Maple notation 2*(9*n^4+6*n^3+21*n^2-16*n-34)*2^(1/2)/(2^n*n*(2*n^3+n-3))^(1/2)/(2*n^2+2*n+3) This took, 0.237, seconds. The, 4, moment about the mean of the r.v. number of edges contained in the tr\ uth table of a random Boolean function is n n 6 n 5 6 n 4 5 n 3 2 n (n - 1) (12 2 n + 12 2 n + 520 n + 24 2 n - 24 n - 12 2 n 4 n 2 3 n 2 + 1272 n - 9 2 n - 840 n - 27 2 n - 5232 n - 2768 n + 240)/4194304 and in Maple notation 1/4194304*2^n*n*(n-1)*(12*2^n*n^6+12*2^n*n^5+520*n^6+24*2^n*n^4-24*n^5-12*2^n*n ^3+1272*n^4-9*2^n*n^2-840*n^3-27*2^n*n-5232*n^2-2768*n+240) hence the scaled, 4, moment is 6 5 (-n) 6 4 (-n) 5 3 (-n) 4 (12 n + 12 n + 520 2 n + 24 n - 24 2 n - 12 n + 1272 2 n 2 (-n) 3 (-n) 2 (-n) (-n) - 9 n - 840 2 n - 27 n - 5232 2 n - 2768 2 n + 240 2 ) / 2 2 / (n (n - 1) (2 n + 2 n + 3) ) / and in Maple notation 1/n/(n-1)/(2*n^2+2*n+3)^2*(12*n^6+12*n^5+520*2^(-n)*n^6+24*n^4-24*2^(-n)*n^5-12 *n^3+1272*2^(-n)*n^4-9*n^2-840*2^(-n)*n^3-27*n-5232*2^(-n)*n^2-2768*2^(-n)*n+ 240*2^(-n)) This took, 176.284, seconds. This took, 176.593, seconds .