Probability and Statistics: Volume I

Who is a probabilist? Someone who knows the odds of drawing an ace of diamonds, or the waiting time at a ticket office? A mathematician who uses a special vocabulary? And who is a statistician? Someone who is capable of determining whether tobacco encourages cancer, or the number of votes which a certain candidate will poll at the next elections? Each one perceives the link: chance. The probabilist, guided by his intuition of poker or queues, constructs an abstract model; having fixed the mathematical framework, he calmly follows through his logical reasoning, which sometimes him very far from his starting point. The statistician takes works on solid ground. When a doctor asks him if it is worth using a new drug, he uses the tools of a probabilist. However he must reach a decision, the least harmful option, based on analyzing the doctor's observations, while taking into account the various risks involved. In short, a probabilist keeps his hands clean while dreaming of models, while a statistician must dirty his hands while working with concrete facts. Relations between the two have often been difficult; but the barriers to their dialogue are broken down by the interest in the concrete to supplement theoretical dreams or in complicated models to describe various phenomena. However, few students have a chance to overcome these barriers.