Related Experiment Video
Updated: Nov 27, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
Published on: September 19, 2012
Memories of the Future. Predictable and Unpredictable Information in Fractional Flipping a Biased Coin
1Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA.
Abstract:
Some uncertainty about flipping a biased coin can be resolved from the sequence of coin sides shown already. We report the exact amounts of predictable and unpredictable information in flipping a biased coin. Fractional coin flipping does not reflect any physical process, being defined as a binomial power series of the transition matrix for "integer" flipping. Due to strong coupling between the tossing outcomes at different times, the side repeating probabilities assumed to be independent for "integer" flipping get entangled with one another for fractional flipping. The predictable and unpredictable information components vary smoothly with the fractional order parameter. The destructive interference between two incompatible hypotheses about the flipping outcome culminates in a fair coin, which stays fair also for fractional flipping.
More Related Videos
08:24The Joint Effect of Social Comparison and Social Distance on Evaluation of Intertemporal Choice Outcomes in Event-related Potential Studies
Published on: August 25, 2023
16:23Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction
Published on: February 26, 2014
Related Concept Videos
Bias
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...
Probability in Statistics
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Binomial Probability Distribution
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Random Error
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Probability Distributions
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...