PROBABILITY AT STATS:

Let X ~ fx;e be a random variable with distribution fx: with unknown param- eter 0 that lives in the parameter space 2. Suppose we are given a sample (x1, X2, . . . , Xn) of X. For each subset Q' c 2 of the parameter space, we define its maximum likelihood as L(S') = L(X1, . .., Xn; ') := sup L(x1, . . ., Xn;0 = 0'). Fix 20 CQ and let 21 = 2\\20. Fix a constant 0