PHY.8:2 - Problem

A correct average can answer the wrong physical question. A detector saturates on individual excursions, not on the ensemble mean. A system prepared in one part of its state space need not explore all alternatives during the observation. Separate constituents can share a preparation that makes their fluctuations add together.

The weighting is also a physical choice. Counting possible states does not by itself make them equally probable. Fitting a distribution to a signal does not establish the microscopic mechanism that produces it. A numerical sequence can sample the desired distribution without representing the time evolution of the system.

The task is to carry physical preparation and interaction through the statistical construction to the consequence that will be used.