Probability problems

Problem of points

The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value. The problem concerns a game of chance with two players who have equal chances of winning each round. The players contribute equally to a prize pot, and agree in advance that the first player to have won a certain number of rounds will collect the entire prize. Now suppose that the game is interrupted by external circumstances before either player has achieved victory. How does one then divide the pot fairly? It is tacitly understood that the division should depend somehow on the number of rounds won by each player, such that a player who is close to winning will get a larger part of the pot. But the problem is not merely one of calculation; it also involves deciding what a "fair" division actually is. (Wikipedia).

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C72 What to do about the singular point

Now that we can calculate a solution at analytical points, what can we do about singular points. It turns out, not all singular points are created equal. The regular and irregular singular point.

From playlist Differential Equations

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How to find + classify critical points of functions

Download the free PDF http://tinyurl.com/EngMathYT This video shows how to calculate and classify the critical points of functions of two variables. The ideas involve first and second order derivatives and are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

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What is a fixed point?

In this video, I prove a very neat result about fixed points and give some cool applications. This is a must-see for calculus lovers, enjoy! Old Fixed Point Video: https://youtu.be/zEe5J3X6ISE Banach Fixed Point Theorem: https://youtu.be/9jL8iHw0ans Continuity Playlist: https://www.youtu

From playlist Calculus

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Finding critical points of functions

Download the free PDF http://tinyurl.com/EngMathYT This is an example illustrating how to find and classify the critical points of functions of two variables. Such ideas rely on the second derivative test and are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

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How to find and classify critical points of functions

Download the free PDF from http://tinyurl.com/EngMathYT This video shows how to calculate and classify the critical points of functions of two variables. The ideas involve first and second order derivatives and are seen in university mathematics.

From playlist Mathematics for Finance & Actuarial Studies 2

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Tangent Line Problem

This video is a brief overview of the classic calculus problem, "The Tangent Line Problem." This problem is a typical introduction to to the topic of calculus, along with "The Area Problem." Course: Calculus I Book reference: Calculus, 9e. By Ron Larson and B. Edwards. Chapter 1.1 Ques

From playlist Calculus I

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The Corner Cube Problem

The corner cube problem is interesting because it initially looks difficult. When the problem was first posed to me, for example, it didn't know how to solve it. Still, my intuition bells were ringing, telling me there was a nice solution. In this video, I cover two of these solutions, in

From playlist Fun

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How to find critical points of functions

Download the free PDF from http://tinyurl.com/EngMathYT This is an example illustrating how to find and classify the critical points of functions of two variables. Such ideas rely on the second derivative test and are seen in university mathematics.

From playlist Mathematics for Finance & Actuarial Studies 2

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Stability of Critical Points (Differential Equations 37)

Using Critical Points to determine increasing and decreasing of general solutions to differential equations.

From playlist Differential Equations

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The Complexity of Gradient Descent: CLS = PPAD ∩ PLS - Alexandros Hollender

Computer Science/Discrete Mathematics Seminar I Topic: The Complexity of Gradient Descent: CLS = PPAD ∩ PLS Speaker: Alexandros Hollender Affiliation: University of Oxford Date: October 11, 2021 We consider the problem of computing a Gradient Descent solution of a continuously different

From playlist Mathematics

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Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture I

Over the past decade interior point methods (IPMs) have played a pivotal role in mul- tiple algorithmic advances. IPMs have been leveraged to obtain improved running times for solving a growing list of both continuous and combinatorial optimization problems including maximum flow, bipartit

From playlist Summer School on modern directions in discrete optimization

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23. Acid-Base Titrations Part I

MIT 5.111 Principles of Chemical Science, Fall 2014 View the complete course: https://ocw.mit.edu/5-111F14 Instructor: Catherine Drennan A common chemistry laboratory experiment involves titrating a strong base into a weak acid, drop by drop, until a color change of an indicator dye tells

From playlist MIT 5.111 Principles of Chemical Science, Fall 2014

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The deterministic communication complexity of approximate fixed point - Weinstein

Computer Science/Discrete Mathematics Seminar Topic: The deterministic communication complexity of approximate fixed point Speaker: Omri Weinstein Date: Monday, February 22 We study the two-party communication complexity of the geometric problem of finding an approximate Brouwer fixed-po

From playlist Mathematics

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Mathematical Games Hosted by Ed Pegg Jr. [Episode 1: Collection of Points and Lines]

Join Ed Pegg Jr. as he explores a variety of games and puzzles using Wolfram Language. In this episode, he features games and puzzles using points and lines. 2:36 Ed begins talking Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebo

From playlist Mathematical Games Hosted by Ed Pegg Jr.

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Lecture 22: Optimization (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

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Mod-01 Lec-12 Solving ODE - BVPs Using Firute Difference Method

Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org

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Lec 24 | MIT 5.111 Principles of Chemical Science, Fall 2005

Acid Base Titrations and Oxidation/Reduction (Prof. Catherine Drennan) View the complete course: http://ocw.mit.edu/5-111F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 5.111 Principles of Chemical Science, Fall 2005

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Mod-01 Lec-14 Finite Difference Method (contd.) and Polynomial Interpolations

Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org

Related pages

Pascal's triangle | Expected value | Probability theory | Christiaan Huygens | Pierre de Fermat | Odds | Luca Pacioli | Mathematical induction | Combination