Sufficient statistics, a lossless summary for a parameter
Asked at DE Shaw
Define a sufficient statistic, prove that is sufficient for the Bernoulli (and Poisson) parameter, and explain why sufficiency matters for estimation.
Show a hint
Sufficiency is easiest to check not from the definition but from how the likelihood factorizes.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.