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Sunday, January 15, 2006

Puzzle: Sum of Uniformly Distributed Random Numbers

I have just added a document to the site, Sum of Uniformly Distributed Random Numbers, which I've been developing off and on (mostly off—the duty cycle is barely distinguishable from zero) for about a year. At the moment, it is linked neither to the home page nor the navigation tree, but exclusively to this update log item. Since folks who peruse these pages are disproportionately “bleeding edge” early adopters and even more persnickety and critical (qualities I hold in the highest esteem when it comes to reviewing documents) than the general audience Fourmilab attracts, I thought I'd open up the new document to your scrutiny before inviting the general public to visit it. (I'll probably make this a general practice for new additions to the site unless this experiment results in no useful feedback.)

Without giving away the answer, I believe this document could be improved both by additional intuitive analyses and by a crystal-clear explanation of how the crucial integral (you'll know which one I'm speaking of when you read the answer) is evaluated, as opposed to the present description which amounts to saying “abracadabra”.

Apart from the content, this document is my first excursion into the ascetic world of XHTML-1.0-Strict document construction. Writing a Strict-compliant document sometimes feels like scribbling with John Calvin looking over your shoulder, ready to administer a severe chastisement the moment a transitory weakness should cause you to indulge in such frivolity as a <font> tag or an align= attribute. Just when you think you've arrived at a modus vivendi with W3C fundamentalism, you discover that the target= attribute in links has been excommunicated on the grounds that it is a “presentation issue” . This capability is supposed to be reinstated by the target module in XHTML 1.1, but that isn't the version most installed browsers support these days. So, there's an awful JavaScript/DOM kludge one employs to fake the effect of the target= attribute; if JavaScript is absent or disabled or the browser doesn't sufficiently support DOM, the worst that happens is that the targeted links open in the main browser window. That, I suppose may be called a “presentation issue”.

Posted at January 15, 2006 22:04