Prague, Czech Republic

Probability and Mathematical Statistics

Pravděpodobnost a matematická statistika

Language: Czech Studies in Czech
Subject area: mathematics and statistics
University website: www.cuni.cz
Years of study: 4
Mathematical Statistics
Mathematical statistics is the application of mathematics to statistics, as opposed to techniques for collecting statistical data. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.
Probability
Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.
Statistics
The individual source of the statistics may easily be the weakest link. Harold Cox tells a story of his life as a young man in India. He quoted some statistics to a Judge, an Englishman, and a very good fellow. His friend said, Cox, when you are a bit older, you will not quote Indian statistics with that assurance. The Government are very keen on amassing statistics—they collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But what you must never forget is that every one of those figures comes in the first instance from the chowty dar [chowkidar] (village watchman), who just puts down what he damn pleases.
Josiah Stamp, recounting a story from Harold Cox, Some Economic Factors in Modern Life (1929), p. 258.
Probability
In applying dynamical principles to the motion of immense numbers of atoms, the limitation of our faculties forces us to abandon the attempt to express the exact history of each atom, and to be content with estimating the average condition of a group of atoms large enough to be visible. This method... which I may call the statistical method, and which in the present state of our knowledge is the only available method of studying the properties of real bodies, involves an abandonment of strict dynamical principles, and an adoption of the mathematical methods belonging to the theory of probability. … If the actual history of Science had been different, and if the scientific doctrines most familiar to us had been those which must be expressed in this way, it is possible that we might have considered the existence of a certain kind of contingency a self evident truth, and treated the doctrine of philosophical necessity as a mere sophism.
James Clerk Maxwell, "Introductory Lecture on Experimental Physics," The Scientific Papers of James Clerk Maxwell (1890) Vol. 2.
Probability
How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?
Sherlock Holmes Sign of the Four Chap. 6, p. 111, written by Arthur Conan Doyle
An EU project improved recycling of agricultural plastics film waste. The group developed a logistics system, also a three-stage process for on-site removal of earth and rocks from the film, involving a dry airflow technology.
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