Corollary: An estimation obstruction for this pair

For the pair in Proposition prop:overlap, no record-only estimator has both probabilities

greater than $1/2$ when $\epsilon <|{\theta }^{(0)}-{\theta }^{(1)}|/2=1/100$.

Proof. The two success intervals are disjoint. Under the common data law, and any common randomized estimator, their probabilities sum to at most one.