Ex 10.2: precision P(R=1 | v=1) = a p / (a p + f (1-p)) and recall a, for a = 0.9, f = 0.1
       p  precision
    0.01     0.0833
    0.05     0.3214
     0.2     0.6923
     0.5     0.9000
     0.9     0.9878

Ex 10.3: squared correlation between v and R under symmetric flips: (1-2 eps)^2 p(1-p) / (q(1-q)),  q = eps + (1-2 eps) p
      p eps=0.0   eps=0.1   eps=0.25  eps=0.4  
   0.05    1.0000    0.2525    0.0596    0.0079
    0.3    1.0000    0.5989    0.2188    0.0338
    0.5    1.0000    0.6400    0.2500    0.0400

Ex 10.7: probability that a group of G has at least one success, and the expected number of steps until one does
       p            G=4            G=8           G=16           G=32
     0.1  0.344 /   2.9  0.570 /   1.8  0.815 /   1.2  0.966 /   1.0
    0.03  0.115 /   8.7  0.216 /   4.6  0.386 /   2.6  0.623 /   1.6
    0.01  0.039 /  25.4  0.077 /  12.9  0.149 /   6.7  0.275 /   3.6
   0.003  0.012 /  83.7  0.024 /  42.1  0.047 /  21.3  0.092 /  10.9

Ex 10.8: variance of the leave-one-out advantage when the verifier flips a binary reward with probability eps
      p   eps    G  simulated  formula q(1-q)(1+1/(G-1))
    0.3   0.0    8     0.2396                     0.2400
    0.3   0.1    8     0.2567                     0.2565
    0.3  0.25    8     0.2744                     0.2743
    0.3  0.25    2     0.4798                     0.4800
   0.05   0.1   16     0.1286                     0.1284
