3. Estimate

3.1 Introduction

The problem of statistics is as follows: a random variable is observed, the distribution of which is – completely or partially – unknown. The aim is to obtain as much information as possible about this distribution from a sample of observations.

Example

Let's assume that parts are manufactured on a machine. All the parts manufactured have the same unknown probability θ of being defective. 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, θ = 0 is never achieved. Before starting the manufacturing cycle, we want to check whether the machine is "well set", i.e. whether θ is small enough. To do this, we produce a certain...

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Estimate