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# Name:Treasa Bency Biju Jose
# Date: 10-06-2020
# Assignment #12
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1. 
CP1 := proc(L) local R, i; option remember; 
R := L[1]; 
for i from 2 to nops(L) do 
 R := CP(R, L[i]); 
end do; 
R; 
end proc;

P := [[1, 2, 3, 4], [5, 6, 7, 8]];
               P := [[1, 2, 3, 4], [5, 6, 7, 8]]

CP1(P);
     [6, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 11, 9, 10, 11, 12]

CP([1, 2, 3, 4], [5, 6, 7, 8]);
     [6, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 11, 9, 10, 11, 12]

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2.
w := [1, 2, 3, 4];
                       w := [1, 2, 3, 4]


AveGF := proc(f, x) 
subs(x = 1, diff(f, x))/subs(x = 1, f); 
end proc;

kthMomentGF := proc(f, x, k) local mu, f1, i; 
mu := AveGF(f, x); 
f1 := f/(x^mu*subs(x = 1, f)); 
for i to k do 
  f1 := expand(x*diff(f1, x)); 
end do; 
subs(x = 1, f1); 
end proc;

g := WtEn(w, x);
                           4    3    2    
                     g := x  + x  + x  + x

evalb(kthMomentGF(g, x, 2) = kthMomentClever(w, 2));
                              true

evalb(AveGF(g, x) = AveClever(w));
                              true
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3.
ScaledMomentGF := proc(f, x, k) local mu, f1, i; 
mu := AveGF(f, x); 
f1 := f/(x^mu*subs(x = 1, f)); 
for i to k do 
   f1 := expand(x*diff(f1, x)); 
end do; 
subs(x = 1, f1); 
end proc;

ScaledMomentGF(m_k(X)/m_2(X)^(k/2), x, 2);
                         -15 ln(m_2(X))

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4.
d := [seq(ScaledMomentGF(((x + 1)/2)^n, x, k), k = 2 .. 10)];
         [1         1     3   2     1     15  3   15  2     
    d := [- n, 0, - - n + -- n , 0, - n + -- n  - -- n , 0, 
         [4         8     16        4     64      32        

        17     105  4   105  3   147  2     
      - -- n + --- n  - --- n  + --- n , 0, 
        16     256      64       64         

      31     1575  4   4095  3   1185  2   945   5]
      -- n - ---- n  + ---- n  - ---- n  + ---- n ]
      4      256       256        64       1024   ]


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