- published: 25 Dec 2011
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Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. 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.
It is not possible to predict precisely results of random events. However, if a sequence of individual events, such as coin flipping or the roll of dice, is influenced by other factors, such as friction, it will exhibit certain 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.
Concepts. Probability formulas. Examples with decks of cards, marbles and Venn diagrams. Addition rule. For more free math videos, visit: http://www.professorserna.com
MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013 View the complete course: http://ocw.mit.edu/18-S096F13 Instructor: Choongbum Lee This lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem. *NOTE: Lecture 4 was not recorded. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Basics of Set Theory for Probability
In this video, I go over the definition of an event and a sample space, i discuss the importance of setting your sample space, I go over the three axioms of probability and use an example with dice as an application
The history of probability theory is introduced. We visit ideas developed by Cardano, Pascal and Fermat. Gambling motivated an evolved perspective on random sequences of events. The concept of frequency stability will play an important role years later in our story....
This lecture explains the reasons why we use the language of measure theory to do probability theory. The key point is that the undergraduate notions of probability density function (p.d.f.) and cumulative density function (c.d.f) are "density focused" and aren't so useful when considering more general probabilistic objects such as randomly generated functions. I then go on to give a brief introduction to probability measures. There are a million introductions to measure-theoretic probability out there, but I wanted to give one to address the complaints that many people (including myself) have, namely "Why should we care?" and "Why are sigma algebras and measures defined the way they are?" This was originally the first lecture in the Advanced Probability class I taught at the University...
Fermat and Pascal played a coin flipping game. Fermat got 1 point if the coin showed heads, and Pascal got 1 point if if the coin showed tails. The first to 10 points won a prize of 100 francs. At a score of 8-7 with Fermat leading, the game was interrupted and could not be resumed. They agreed to split the prize fairly. What percentage of the prize should each person get? This story took place around 1654 and is known as the problem of the points. It helped develop some fundamental concepts in probability theory in determining fair stakes for a gamble. In the video I present two methods to solve this problem. Blog post (text explanation): http://wp.me/p6aMk-4se Problem of the points: http://mathforum.org/isaac/problems/prob1.html Thanks to Patrons! Kyle Alberto Nishikawa Brian M. Moon...
What probability is. More free lessons at: http://www.khanacademy.org/video?v=3ER8OkqBdpE
Understanding Probability (Basic tutorial) http://www.garguniversity.com
In this video I explain the difference between theoretical and experimental probability
Get your free audiobook or ebook: http://yazz.space/mabk/30/en/B001G60JFS/book Patrick Suppes is a philosopher and scientist whose contributions range over probability and statistics, mathematical and experimental psychology, the foundations of physics, education theory, the philosophy of language, measurement theory, and the philosophy of science. He has also been a pioneer in the area of computer assisted instruction. In each of these areas, Suppes has provided seminal ideas that in some cases led to shaping the direction of research in the field. The papers contained in this collection were commissioned with the mandate of advancing research in their respective fields rather than retrospectively surveying the contributions that Suppes himself has made. The authors form an interesting mi...
EARNING METHODS FREE SKILL DEVELOPMENT COURSES SERIES CHANNEL CHAPTER- 9 Review of Probability Theory and Random Process_low FREE VIDEO TRAINING PROGRAMS अगर आप सभी इस तरह के कोर्सेज फ्री में करना चाहते है तो निचे कमेंट बॉक्स में जरूर लिखे और बताये आप लोगो को किस तरह के कोर्सेस करना चाहते है , हम पूरी कोशिश करेंगे आप सभी के लिए उसे उपलब्ध करा सके educational technology lectures free Digital Electronics Course online series पयारे दोस्तों हमारा ये ग्रुप EARNING METHODS" इस चैंनल में आप सभी " INFORMATION TECHNOLOGY" से जुड़े अलग-२ विडियो के सीरीज के माध्यम से आप बहुत कुछ सिख पाएंगे , जिसमे information technology, {ANALOG DIGITAL,COMMUNICATION, CONTROL SYSTEM,ECONOMICS LECTURE'S ,BIOLOGY ENERGY, Ecology, Environment and Ecosystem - Environment आदि } बहूत सारे कोर्सेज की सीरीज़ होगी...
Learning Theory (Reza Shadmehr, PhD) Bayes rule, expected value and variance of random variables and sum of random variables, expected value of random variables raised to a power, Binomial distribution, Poisson distribution, Normal distribution.
Probability is the examination of uncertain processes, but it's useful for far more than games of chance: http://www.gresham.ac.uk/lectures-and-events/probability-and-its-limits The modern theory of probability is considered to have begun in 1654 with an exchange of letters between Blaise Pascal and Pierre de Fermat, and has developed since then into the discipline which examines uncertain processes. For example, although on tossing a coin you have no idea whether you will obtain heads or tails we know that if you keep doing it then in the long run it is very likely that the proportion of heads will be close to a half. The lecture will discuss this and other examples of random processes e.g. random walks and Brownian motion. The transcript and downloadable versions of the lecture are ava...
CDT Easter School 2015 Fundamentals of Numerical Methods for Uncertainty Quantification and the Analysis of Complex Systems Lecture video 1.2 (day 1, 13th April)
Mechanical Engineering 233 - Spring 2014: Advanced Control Systems II Creative Commons 3.0: Attribution-NonCommercial-NoDerivs
October 21, 2010 - In recent years, probability theory has come to play an increasingly important role in computing. Professor Sahami gives examples of how probability underlies a variety of applications on the Internet including web search and email spam filtering. This lecture is offered as part of the Classes Without Quizzes series at Stanford's 2010 Reunion Homecoming. Mehran Sahami, PhD, is an associate professor of computer science and the department's associate chair for education. Prior to joining the Stanford faculty, he was a Senior Research Scientist at Google. Stanford University: http://www.stanford.edu/ Stanford Alumni Association: http://www.stanfordalumni.org/ Computer Science at Stanford: http://www-cs.stanford.edu/ Stanford University Channel on YouTube: http://www.y...
Introductory lecture on Probability Theory: The Logic of Science by E.T. Jaynes. Aubrey Clayton, March 2015
Lecture 2 covering Chapter 1: "Plausible reasoning" from Probability Theory: The Logic of Science by E.T. Jaynes. Aubrey Clayton, March 2015