On One Problem of Observation Control

he problem of estimating an unknown parameter $\theta\in[0,1]$ by a confidence interval is considered. If points $x$, $y\in[0,1]$ are chosen as observation points, then the device in question indicates whether the estimated parameter belongs to the segment $[x,y]$ or not, but it has an error probability $p$. An observation strategy with a fixed number of observations is set up and investigated. An asymptotically optimal observation strategy is designed for the problem with a random number of observations.