I have a single observation X from the following distribution: $$P(X=-1) = \frac{p}{3}, P(X=0) = (1-p), P(X=1) = \frac{2p}{3}$$ I'm trying to prove that there is no complete and sufficient statistic for p based on the single observation X, but I'm getting a bit lost on how to do it since it's tricky to show that an estimator can be just one but not the other. Any hints on how to approach this?
2026-04-02 13:58:05.1775138285
Finding complete and sufficient statistic for discrete distribution
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