![Week 3, Lecture 2, Conditional probabilities](http://s1.studyres.com/store/data/008677175_1-e7b7f71b71d89488f34ffc5ba5bfe3b6-300x300.png)
MAS275 Probability Modelling Example 21
... We will model the sequence of squares the player visits as a Markov chain. We start with a very simplified version. Let Xn be the nth square visited by the player. The player starts on square 0 (or 40; labelled “Go”), so X0 = 0. In most cases, if on square j, the player moves to square j + k( mod 40 ...
... We will model the sequence of squares the player visits as a Markov chain. We start with a very simplified version. Let Xn be the nth square visited by the player. The player starts on square 0 (or 40; labelled “Go”), so X0 = 0. In most cases, if on square j, the player moves to square j + k( mod 40 ...
MODERATE DEVIATIONS FOR BOUNDED SUBSEQUENCES
... parameters as in the case of martingale difference or i.i.d. sequences. Copyright © 2006 George Stoica. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work i ...
... parameters as in the case of martingale difference or i.i.d. sequences. Copyright © 2006 George Stoica. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work i ...
WCMC Probability and Statistics `10 FD
... In search for the ancient mathematics knowledge that has been lost since 3141BC, explorers have come to a vault which requires them to place two numbers in the first two spots and two letters in the other two spots. If they can try 200 combinations an hour, how many hours will it take to go through ...
... In search for the ancient mathematics knowledge that has been lost since 3141BC, explorers have come to a vault which requires them to place two numbers in the first two spots and two letters in the other two spots. If they can try 200 combinations an hour, how many hours will it take to go through ...
How To Think Like A Computer Scientist
... The rationals are dense: between any two there is a third. You can’t list them one by one without leaving out an infinite number of them. ...
... The rationals are dense: between any two there is a third. You can’t list them one by one without leaving out an infinite number of them. ...
RESEARCH PROJECTS 1. Irrationality questions
... no pair with a smaller numerator. (It’s a nice exercise to show such a pair exists. One solution is to use a descent argument, which you might have seen in cases of Fermat’s last theorem or elliptic curves.) Then ...
... no pair with a smaller numerator. (It’s a nice exercise to show such a pair exists. One solution is to use a descent argument, which you might have seen in cases of Fermat’s last theorem or elliptic curves.) Then ...
How to Built an Infinite Lottery Machine
... machine, what inductive support does each outcome accrue?2 Because of the problem above, a probability seems unable to measure that support. Most attempts to escape adjust the notion of probability. De Finetti (1972; §5.17) discarded “countable additivity,” the capacity to sum the infinitely many ou ...
... machine, what inductive support does each outcome accrue?2 Because of the problem above, a probability seems unable to measure that support. Most attempts to escape adjust the notion of probability. De Finetti (1972; §5.17) discarded “countable additivity,” the capacity to sum the infinitely many ou ...
Infinite monkey theorem
![](https://commons.wikimedia.org/wiki/Special:FilePath/Monkey-typing.jpg?width=300)
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.