15. Games of Chance - University of Vermont
... The History of Games of Chance Games of chance are rooted in divination. ...
... The History of Games of Chance Games of chance are rooted in divination. ...
Probability - OnlineStatBook
... Inferential statistics is built on the foundation of probability theory, and has been remarkably successful in guiding opinion about the conclusions to be drawn from data. Yet (paradoxically) the very idea of probability has been plagued by controversy from the beginning of the subject to the presen ...
... Inferential statistics is built on the foundation of probability theory, and has been remarkably successful in guiding opinion about the conclusions to be drawn from data. Yet (paradoxically) the very idea of probability has been plagued by controversy from the beginning of the subject to the presen ...
Stochastic Lambda Calculus and Monads of Probability Distributions
... Given properties 1 and 2, it is straightforward to prove that the definitions of return and >>= satisfy the monad laws. To create some interesting distributions, we need at least one more operation in our monad. The choose function is a two-argument version of the dist used in Section 2.1. Probabil ...
... Given properties 1 and 2, it is straightforward to prove that the definitions of return and >>= satisfy the monad laws. To create some interesting distributions, we need at least one more operation in our monad. The choose function is a two-argument version of the dist used in Section 2.1. Probabil ...
What Could Be Objective About Probabilities
... belief dynamics. This is typically done in a normative theory: no one claims that the dynamics of actual belief states of real people would be properly described by that rule. Of course, there are episodes of actual belief change that can be modeled by the rule: save for it being a prediction of str ...
... belief dynamics. This is typically done in a normative theory: no one claims that the dynamics of actual belief states of real people would be properly described by that rule. Of course, there are episodes of actual belief change that can be modeled by the rule: save for it being a prediction of str ...
full text as PDF file
... maximum likelihood estimator, that have the same guaranteed coverage probability. Hence, there is a substantial price to be paid for sparsity, which is not revealed by the pointwise asymptotic analysis underlying the “oracle”property. Special cases of the general results provided in Section 2 have b ...
... maximum likelihood estimator, that have the same guaranteed coverage probability. Hence, there is a substantial price to be paid for sparsity, which is not revealed by the pointwise asymptotic analysis underlying the “oracle”property. Special cases of the general results provided in Section 2 have b ...
Estimating the probability of negative events
... ship between the utility of the outcome and participants’ probability ratings. It is possible, however, that the pragmatics of the situation (i.e., the fact that they were taking part in an experiment) led participants to believe that it was unlikely that they would emerge from the study having to p ...
... ship between the utility of the outcome and participants’ probability ratings. It is possible, however, that the pragmatics of the situation (i.e., the fact that they were taking part in an experiment) led participants to believe that it was unlikely that they would emerge from the study having to p ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.