1. Concrete problem

Suppose a factory manufactures parts on a machine. The diameter of each part depends on the setting of the machine, the better the setting, the closer the diameter of the part is to a d ₀ norm; but as the setting cannot be perfect, we never have exactly d ₀ . The diameter of each part can be modeled by a random variable X. Furthermore, each manufactured part has an unknown probability θ, but the same for all parts, of being defective, i.e. with a diameter greater than the standard d ₀ . This number θ depends on the setting of the machine, the better the setting, the closer θ is to 0; but as the setting cannot be perfect, we never have θ = 0. A certain number n of parts are manufactured to test the setting. The observation consists in measuring the diameter...