Posts Tagged ‘ Probability ’

R: Clash of the cannon cycles

July 19, 2010
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R: Clash of the cannon cycles

Imagine a unit square. Every side has length 1, perfectly square. Now imagine this square was really a fence, and you picked two spots at random along the fence, with uniform probability over the length of the fence. At each of these two locations, set down a special kind of cannon. Just like the light

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100 Prisoners, 100 lines of code

July 9, 2010
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100 Prisoners, 100 lines of code

In math and economics, there is a long, proud history of placing imaginary prisoners into nasty, complicated scenarios. We have, of course, the classic Prisoner’s Dilemma, as well as 100 prisoners and a light bulb. Add to that list the focus of this post, 100 prisoners and 100 boxes. In this game, the warden places

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Those dice aren’t loaded, they’re just strange

June 18, 2010
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Those dice aren’t loaded, they’re just strange

I must confess to feeling an almost obsessive fascination with intransitive games, dice, and other artifacts. The most famous intransitive game is rock, scissors, paper. Rock beats scissors.  Scissors beats paper. Paper beats rock. Everyone older than 7 seems to know this, but very few people are aware that dice can exhibit this same behavior,

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A different way to view probability densities

June 12, 2010
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A different way to view probability densities

The standard, textbook way to represent a density function looks like this: Perhaps you have seen this before? (Plot created in R, all source code from this post is included at the end). Not only will you find this plot in statistics books, you’ll also see it in medical texts, sociology, and even economics books.

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Tuesday’s child is full of probability puzzles

May 28, 2010
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Tuesday’s child is full of probability puzzles

COUNTERINTUITIVE PROBLEM, INTUITIVE REPRESENTATION Blog posts about counterintuitive probability problems generate lots of opinions with a high probability. Andrew Gelman and readers have been having a lot of fun with the following probability problem: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? The

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How many girls, how many boys?

April 30, 2010
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How many girls, how many boys?

I found this interesting question over here at mathoverflow.net. Here’s the question: If you have a country where every family will continue to have children until they get a boy, then they will stop. What is the proportion of boys to girls in the country. First off, there are some assumptions you need to make that aren’t

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A von Mises variate…

March 25, 2010
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A von Mises variate…

Inspired from a mail that came along the previous random generation post the following question rised : How to draw random variates from the Von Mises distribution? First of all let’s check the pdf of the probability rule, it is , for . Ok, I admit that Bessels functions can be a bit frightening, but

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Example 7.27: probability question reconsidered

March 15, 2010
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Example 7.27: probability question reconsidered

In Example 7.26, we considered a problem, from the xkcd blog:Suppose I choose two (different) real numbers, by any process I choose. Then I select one at random (p= .5) to show Nick. Nick must guess whether the other is smaller or larger. Being righ...

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\pi day!

March 14, 2010
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\pi day!

It’s π-day today so we gonna have a little fun today with Buffon’s needle and of course R. A well known approximation to the value of $latex \pi$ is the experiment tha Buffon performed using a needle of length,$latex l$. What I do in the next is only to copy from the following file the function

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Example 7.26: probability question

March 8, 2010
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Example 7.26: probability question

Here's a surprising problem, from the xkcd blog.Suppose I choose two (different) real numbers, by any process I choose. Then I select one at random (p= .5) to show Nick. Nick must guess whether the other is smaller or larger. Being right 50% of the ...

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