Factorisation and data reduction
For iid Bernoulli observations, apply the Fisher–Neyman theorem to prove that S({\boldsymbol{x}})=\sum_i x_i is sufficient. Then use the likelihood-ratio criterion to show that it is minimal sufficient.
For iid Bernoulli observations, apply the Fisher–Neyman theorem to prove that S({\boldsymbol{x}})=\sum_i x_i is sufficient. Then use the likelihood-ratio criterion to show that it is minimal sufficient.
This exercise has no worked answer.