Ex 7.1: P(r1 + g1 > r2 + g2) with i.i.d. Gumbel noise equals sigma(r1 - r2)
  r1 - r2 = 0.0: simulated 0.4998   sigma = 0.5000
  r1 - r2 = 0.7: simulated 0.6683   sigma = 0.6682
  r1 - r2 = 2.0: simulated 0.8809   sigma = 0.8808

Ex 7.3: existence of the maximum-likelihood estimate for three items
  chain a>b>c:
    loss at  1 x direction: 9.07e-02
    loss at  4 x direction: 2.24e-04
    loss at 16 x direction: 8.44e-15
    ridge 1e-6 minimizer: [ 10.38  -0.   -10.38]
  cycle a>b, b>c, c>a:
    loss at  1 x direction: 9.18e-01
    loss at  4 x direction: 2.68e+00
    loss at 16 x direction: 1.07e+01
    ridge 1e-6 minimizer: [0. 0. 0.]

Ex 7.5: E[G | P] = P / (1 + s^2) for G ~ N(0,1), P = G + eps, eps ~ N(0, s^2)
  s = 0.5: regression slope 0.7998 vs 1/(1+s^2) = 0.8000;  mean G given P near 1.5: 1.202 vs 1.200
  s = 1.0: regression slope 0.5002 vs 1/(1+s^2) = 0.5000;  mean G given P near 1.5: 0.747 vs 0.750
  s = 2.0: regression slope 0.1998 vs 1/(1+s^2) = 0.2000;  mean G given P near 1.5: 0.303 vs 0.300

Ex 7.8: symmetric label flips with probability eps; the fitted centered scores regressed on the true ones
  eps = 0.0: slope of fitted on true = 0.999   rank correlation = 1.000
  eps = 0.1: slope of fitted on true = 0.706   rank correlation = 1.000
  eps = 0.2: slope of fitted on true = 0.486   rank correlation = 0.997
  eps = 0.3: slope of fitted on true = 0.304   rank correlation = 0.994
