NYU Probability Summer 2009

Probability theory is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.

foundation

the second Earl of Yarborough offered an interesting bet to his whist-playing friends: a thousand to one against them picking up a hand with no card above a nine. Mathematics was on his side since the odds are 1,827 to 1. There is no record that he ever paid off.

The twin birth rate in the United States in 2004, 2005 and 2006 was slightly above 32 twin live births per 1,000 live births

The twin birth rate in the United States in 2004, 2005 and 2006 was slightly above 32 twin live births per 1,000 live births[2].