Bayesian inference | Coin flipping | Statistical tests
In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials. A fair coin is an idealized randomizing device with two states (usually named "heads" and "tails") which are equally likely to occur. It is based on the coin flip used widely in sports and other situations where it is required to give two parties the same chance of winning. Either a specially designed chip or more usually a simple currency coin is used, although the latter might be slightly "unfair" due to an asymmetrical weight distribution, which might cause one state to occur more frequently than the other, giving one party an unfair advantage. So it might be necessary to test experimentally whether the coin is in fact "fair" – that is, whether the probability of the coin's falling on either side when it is tossed is exactly 50%. It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or "biased") coin to happen to turn up exactly 10 heads in 20 flips. Therefore, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process, given only a limited sample of Bernoulli trials. (Wikipedia).
Determine A Light Coin Among Six Identical Coins In Two Weighings
This video explains how to determine which coin out of 6 identical coins is light using only 2 weighings on a balance scale.
From playlist Mathematics General Interest
HARD Logic Puzzle - The Seemingly Impossible Counterfeit Coin Problem
An evil warden holds you prisoner, but offers you a chance to earn your freedom. You are given 101 coins, of which 51 are genuine and 50 are counterfeit. Each genuine coin is identical. And each counterfeit coin is identical to a genuine coin, except that it differs in weight by exactly 1
From playlist Logic Puzzles And Riddles
Stars and Bars: Determine the Number of Outcomes of 7 Coins of 4 Types
This video explains how to use the stars and bars method of counting to solving a counting problem. mathispower4u.com
From playlist Counting (Discrete Math)
For more details, see http://thedicelab.com/BalancedStdPoly.html These dice are available from http://www.mathartfun.com/DiceLabDice.html
From playlist Dice
Ryan Morrill - Playing Nice with a Weighted Coin - G4G13 Apr 2018
We will investigate an interesting combinatorial problem in constructing a fair game of chance using an unfair coin.
From playlist G4G13 Videos
Money Blender - Iron in a Dollar Bill
U.S. dollar bills are printed with special inks that contain traces of iron and other magnetic material in an effort to prevent counterfeiting. So, the only logical question that follows is, "Can you get the iron out of a dollar bill?" Steve Spangler accepted the challenge with the help of
From playlist Don't try this at home!
This video introduced fair division. Site: http://mathispower4u.com
From playlist Fair Division
Ex: Determine the Outcomes Rolling Colored Dice - Counting Principle
This video explains how to use the counting principle to determine the number of outcome of rolling four colored dice. Site: http://mathispower4u.com
From playlist Counting Principle
4.3.3 Mutual Independence: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Year 12/AS Statistics Chapter 7.1 (Hypothesis Testing)
This video introduces the concept of Hypothesis Testing. We take a careful, detailed look at two cases (an experiment and a sample) and talk through the logic ideas behind hypothesis testing, introducing some important definitions and key terms as we go. This lesson is meant as preparatio
From playlist Year 12/AS Edexcel (8MA0) Mathematics: FULL COURSE
What are p-values?? Seriously.
See all my videos at https://www.zstatistics.com/videos 0:00 Intro 2:00 Coin example 8:52 History of p-values 13:06 One-tailed vs two-tailed p-values 20:02 Example of p-values in journal articles Research article: Si, Y., Xiao, X., Xia, C., Guo, J., Hao, Q., Mo, Q., ... & Sun, H. (2020).
From playlist Health Stats IQ
The Most Powerful Tool Based Entirely On Randomness
We see the effects of randomness all around us on a day to day basis. In this video we’ll be discussing a couple of different techniques that scientists use to understand randomness, as well as how we can harness its power. Basically, we'll study the mathematics of randomness. The branch
From playlist Classical Physics by Parth G
Tutorial 5.2: Tomer Ullman - Church Programming Language Part 2
MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 View the complete course: https://ocw.mit.edu/RES-9-003SU15 Instructor: Tomer Ullman Learn the Church programming language, which facilitates the implementation and testing of generative models of physical and social worl
From playlist MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015
7. Parametric Hypothesis Testing
MIT 18.650 Statistics for Applications, Fall 2016 View the complete course: http://ocw.mit.edu/18-650F16 Instructor: Philippe Rigollet In this lecture, Prof. Rigollet talked about parametric hypothesis testing and discussed Cherry Blossom run and clinical trials as examples. License: Cre
From playlist MIT 18.650 Statistics for Applications, Fall 2016
A-Level Maths: O2-01 [Binomial Hypothesis Testing: Less Than Example 1]
Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ My LIVE Google Doc has the new A-Level Maths specification and
From playlist A-Level Maths Statistics
Powered by https://www.numerise.com/ Independent events
From playlist Multiple event probability
Analysis of the federal reserve balance sheet as of Feb 2007. More free lessons at: http://www.khanacademy.org/video?v=MILF-9GeMDQ
From playlist Banking and Money
EEVblog #1062 - Trezor Model T Hardware Wallet Review
Unboxing and review of the new Trezor Model T cryptocurrency bitcoin hardware wallet. And a comparison with the Ledger Nano S. Also a talk on Ethereum contracts, Myetherwaller and ICO's Crypto Currency: https://www.eevblog.com/crypto-currency/ https://kit.com/EEVblog/crypto-hardware Hard
From playlist Cryptocurrency