## Posts Tagged 'Probability'

### Twin Peaks Entropy

Next week there will be a post on tuning pianos using a method based on entropy. In preparation for that, we consider here how the entropy of a probability distribution function with twin peaks changes with the separation between the peaks.

### Buffon was no Buffoon

The Buffon Needle method of estimating ${\pi}$ is hopelessly inefficient. With one million throws of the needle we might expect to get an approximation accurate to about three digits. The idea is more of philosophical than of practical interest. Buffon never envisaged it as a means of computing ${\pi}$.

Image drawn with Mathematica package in: Siniksaran, Erin, 2008: Throwing Buffon’s Needle [Reference below].

Continue reading ‘Buffon was no Buffoon’

### Bent Coins: What are the Odds?

If we toss a fair’ coin, one for which heads and tails are equally likely, a large number of times, we expect approximately equal numbers of heads and tails. But what is approximate’ here? How large a deviation from equal values might raise suspicion that the coin is biased? Surely, 12 heads and 8 tails in 20 tosses would not raise any eyebrows; but 18 heads and 2 tails might.

This week, That’s Maths in The Irish Times ( TM044 ) is about the originator of Students t-distribution.

In October 2012 a plaque was unveiled at St Patrick’s National School, Blackrock, to commemorate William Sealy Gosset, who had lived nearby for 22 years. Sir Ronald Fisher, a giant among statisticians, called Gosset “The Faraday of Statistics”, recognising his ability to grasp general principles and apply them to problems of practical significance.

Plaque at St Patrick’s National School, Hollypark, Blackrock, where William Gosset lived from 1913 to 1935.

### Breaking Weather Records

In arithmetic series, like 1 + 2 + 3 + 4 + 5 + … , each term differs from the previous one by a fixed amount. There is a formula for calculating the sum of the first N terms. For geometric series, like 3 + 6 + 12 + 24 + … , each term is a fixed multiple of the previous one. Again, there is a formula for the sum of the first N terms of such a series. Continue reading ‘Breaking Weather Records’

### Bayes Rules OK

This week, That’s Maths ( TM018 ) deals with the “war” between Bayesians and frequentists, a long-running conflict that has now subsided. It is 250 years since the presentation of Bayes’ results to the Royal Society in 1763.

The column below was inspired by a book, The Theory that would not Die, by Sharon Bertsch McGrayne, published by Yale University Press in 2011.