A probability puzzle

rall

I saw a ‘simple’ puzzle on the internet which I thought I’d have a crack at in an evening. Several furious scribblings on the bus and the sofa later, I finally have an answer. I’m so relieved I can’t help but share the joy.

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Stochastic geometry and the London underground

PoissonPoints

Way back when I was analysing London house price data for the Summer Data Challenge, I made a histogram of the distances from a random point in London to the nearest tube station. I noted that it peaked around half a kilometre, but ignored the shape of the distribution itself. This is an unfortunate faux pas for the accomplished procrastinator, so let’s right that wrong with the help of some stochastic geometry.

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One Year In: Thanks a Million

I’ve been a little busy recently for blog posts, what with a pesky thesis to finish and all, but such an occasion as this deserves the highest honour possible – making lots of plots. That’s right, the hallowed HTML files under this domain name have been yanked from a poor WordPress server somewhere over 1 million times now, almost coinciding with the first anniversary of the blog. I think it’s a useful event to prompt some details for those of you interested in the business of blogging – who knows, perhaps you’ll start one of your own?

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Fear of heights

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I am a short man. I have an even shorter girlfriend. Odds are, any offspring would be short. Odds are, their partners would be similar or smaller in height, especially if they are male. Does this mean I am destined to be the heir to a slowly shrinking troglodyte race, my pristine DNA squirted from troll to troll until it degrades to a corrosive, fetid broth? Let’s put the thesaurus away and have a look.

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Two Come Along at Once

NextvsSubsequentAnnotated

As the old saying goes, you wait ages for a bus and then two come along at once (or more!). Is this true though? My own anecdotal evidence would suggest yes, every single bloody time. However, we love data and maths in this blog almost as much as we hate waiting for the bus, so let’s have a more thorough look at the issue.

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Bayes vs. Paul the Psychic Octopus

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Paul the octopus, for the unaware, was a true hero of the modern age. Combining cephalopodian good looks with a pragmatically sensible German name, he was the star of the show at the Oberhausen Sea Life Centre. That is, however, until his tragic passing in 2010, when the world lost one of its most famous psychic entities. Over the previous two year period, Paul correctly guessed the outcomes of 12 out of 14 international football matches. Does this merit his psychic status? Let’s investigate, following this great example from the excellent book ‘Statistical Inference for Everyone‘ by Brian Blais.

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