数学专业英语－Probability
The mathematics to which our youngsters are expod at school is. With rare exceptions, bad on the classical yes-or-no, right-or-wrong type of logic. It normally doesn’t include one word about probability as a mode of reasoning or as a basis for comparing veral alternative conclusions. Geometry, for instance, is strictly devoted to the “if-then鸡蛋可以放微波炉加热吗” type of reasoning and so to the notion (idea) that any statement is either correct or incorrect.
However, it has been remarked that life is an almost continuous experience of having to draw conclusions from insufficient evidence, and this is what we have to do when we make the trivial decision as to whether or not to carry an umbrella when we leave home for work. This is what a great industry has to do when it decides whether or not to put $50000000 into a new plant abroad. In none of the ca and indeed, in practically no other ca that you can suggest, can one proceed by saying:” I know that A, B, C, etc. are completely and reliably true, and therefore the inevitable conclusion is~~” For there is another mode of reasoning, which does not say: This statement is correct, and its opposite is completely fals
e.” But which say: There are various alternative possibilities. No one of the is certainly correct and true, and no one certainly incorrect and fal. There are varying degrees of plausibility—of probability—for all the alternatives. I can help you understand how the plausibility’s compare; I can also tell you reliable my advice is.”
This is the kind of logic, which is developed in the theory of probability. This theory deals with not two truth-values—correct or fal—but with all the in intermediate truth values: almost certainly true, very probably true, possibly true, unlikely, very unlikely, etc. Being a preci quantities theory, it does not u phras such as tho just given, but calculates for any question under study the numerical probability that it is true. If the probability has the value of 1, the answer is an unqualified “yes” or certainty. If it is zero (0), the answer is an unqualified “no” i.e. it is fal or impossible. If the probability is a half (0.5), then the chances are even that the question has an affirmative answer. If the probability is tenth (0.1), then the chances are only 1 in 10 that the answer is “yes.”特警力量陶静
It is a remarkable fact that one’s intuition is often not very good at csunating answers to
probability problems. For ex ample, how many persons must there are at least two persons in the room with the same birthday (born on the same day of the month)? Remembering that there are 356 parate birthdays possible, some persons estimate that there would have to be 50, or even 100, persons in the room to make the odds better than even. The answer, in fact, is that the odds are better than eight to one that at least two will have the same birthday. Let us consider one more example: Everyone is interested in polls, which involve estimating the opinions of a large group (say all tho who vote) by determining the opinions of a sample. In statistics the whole group in question is called the “玫瑰花颜色univer红图片” or “population”. Now suppo you want to consult a large enough sample to reflect the whole population with at least 98% precision (accuracy) in 99out of a hundred instances: how large does this very reliable sample have to be? If the population numbers 200 persons, then the sample must include 105 persons, or more than half the whole population. But suppo the population consists of 10,000 persons, or 100,000 persons? In the ca of 10,000 persons, or 1000,000 person? In the ca of 10,000 persons, a sample, to have the stated reliability, would have to consist of 213 pers
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ons: the sample increas by only 108 when the population increas by 9800. And if you add 90000 more to the population, so that it now numbers 100000, you have to add only 4 to the sample. The less credible this ems to you, the more strongly I make the point that it is better to depend on the theory of probability rather than on intuition.
Although the subject started out (began) in the venteenth century with games of chance such as dice and cards, it soon became clear that it had important applications to other fields of activity. In the eighteenth century Laplace laid the foundations for a theory of errors, and Gauss later develop this into a real working tool for all experimenters and obrvers. Any measurement or t of measurement is necessarily is necessarily inexact; and it is a matter of the highest importance to know how to take a lot of necessarily discordant data, combine them in the best possible way, and produce in addition some uful estimate of the dependability of the results. Other more modern fields of application are: in life insurance; telephone traffic problems; information and communication theory; game theory, with applications to all forms of competition, including business international politics and war; modern statistical theories, both for the
efficient design of experiments and for the interpretation of the results of experiments; decision theories, which aid us in making judgments; probability theories for the process by which we learn, and many more.
----Weaver, W.
Vocabulary
Probability 概率论 permutation 置换
Plausibility 似乎合理 binomial coefficient 二次式系数
Affirmative 肯定的 generating function 每夜一个鬼故事母函数
Estimate 估计 even 事件
Discordant 西红柿鸡蛋饼不一致的 information and communication theory
Communication theory 通讯理论 信息与通讯论
Decision theory 决策论 game theory 对策论，博弈论
小泰迪
