Probability

МООК
en
Английский
32 h
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Source
  • From www.coursera.org
Conditions
  • Self-paced
  • Free Access
  • Бесплатный сертификат
More info
  • 8 Sequences
  • Introductive Level

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Course details

Syllabus

The course is divided into five topical segments which taken together constitute a self-contained introduction to mathematical probability.  Read on for a bird's-eye view of these topics.

Topic I: Towards an axiomatic theory of chance

We begin with the stirrings of a mathematical theory in the 17th century in the resolution of a historical wager of the Chevalier de Méré and follow the developments in understanding leading to the modern axiomatic foundations of probability established in the 20th century.

Topic II: From side information to conditional probabilities

In this segment we shall encounter unanticipated challenges to intuition when presented with side information about a probability experiment and discover the subtle importance of additivity in a tongue-in-cheek exhortation on the survival of our species.

Topic III: Independence—the warp and the woof in the fabric of chance

The distinctive and rich intuitive content of the theory of probability and its link to observations in physical experiments is provided by the notion of statistical independence.  We follow the progress from multiplication tables to a formal notion of independence, with enticing applications in a casino game, genetics, and sports psychology to whet the appetite.

Topic IV: From polls to bombs and queues—enter the binomial and the Poisson

We next turn to ruminations on the implausible efficacy of small polls in tracking sentiments of large populations and discover how the hugely important binomial distribution emerges from these considerations.  We then retrace the historical discovery of a curious approximation to the binomial and stumble upon the fascinating Poisson distribution.  We promptly explore applications ranging from the merely weighty to the diverting and macabre, the distribution of bomb hits in London in World War II being particularly memorable.

Topic V: The fabulous limit laws—the bell curve pirouettes into the picture

The law of large numbers is a cornerstone of probability responsible for much of its intuitive content and it is fitting that our gradual development concludes with it.  Among its rich applications, we discover why polls work and the implications to medical testing.  The remarkable bell curve now takes centre stage completing the triad of fundamental distributions and we discover why polls really work.

Prerequisite

None.

Instructors

  • Santosh Venkatesh - Electrical and Systems Engineering

Editor

L'université de Pennsylvanie (communément appelée Penn) fondée en 1740 est une université privée située à Philadelphie, en Pennsylvanie, aux États-Unis. Membre de l'Ivy League, Penn est la quatrième plus ancienne institution d'enseignement supérieur des États-Unis et se considère comme la première université des États-Unis à proposer des études de premier et de deuxième cycle.

Platform

Coursera - это цифровая компания, предлагающая массовые открытые онлайн-курсы, основанные учителями компьютеров Эндрю Нгом и Стэнфордским университетом Дафни Коллер, расположенные в Маунтин-Вью, штат Калифорния.

Coursera работает с ведущими университетами и организациями, чтобы сделать некоторые из своих курсов доступными в Интернете, и предлагает курсы по многим предметам, включая: физику, инженерию, гуманитарные науки, медицину, биологию, социальные науки, математику, бизнес, информатику, цифровой маркетинг, науку о данных и другие предметы.

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