# Statistics Theory Question

Casella& Berger Theorem 6.2.28: If a minimal sufficient statistics exists, any complete statistics is minimal sufficient.

So let's suppose $$X_1...X_n$$ are iid $$Bernoulli(p)$$ $$p\in (0,1)$$, then $$\bar{X}$$ is minimal sufficient statistics. But it seems that $$X_1+X_2$$ is complete since its distribution is Binomial(2,p), but it is not sufficient, let alone minimal sufficient...