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komponisto comments on P(X = exact value) = 0: Is it really counterintuitive? - Less Wrong
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Comments (49)
Only if you have a continuous probability distribution over that domain. It's quite possible to have a probability distribution with, for example, a point mass at 5 such that p(X=5)=0.5.
Others have answered this below, but there is another aspect to this I'd like to discuss. All data are discrete. When you measure something, your measurement apparatus is only ever going to give you one of a discrete, finite set of values. (I'm pretty sure about finite, but willing to be corrected). Any probability distribution over the possible values that you might measure with your apparatus can easily satisfy p(X=x)>0 for all x.
Concretely, if you're measuring the length of something with a ruler, you probably just round to the nearest 1/16th of an inch. This means there are only 12*16=192 possible measurements you can make, so you can create any number of probability distributions of these points where each point has p(X=x)>0.
I implicitly meant a continuous distribution. Clarified that in the post now.
As someone who lives in the dangerous and uncharted part of the world called "outside the US', I prefer centimeters. ;)
Feel free to use centimeters in your own examples, then. But you're not entitled to demand that US users do so.
"I prefer" with a smiley and some mild snark isn't exactly a demand.
In any case, people are entitled to demand whatever they want, they just aren't entitled to get compliance.
Would it be worth having a convention at LW that measurements should be given in English and metric units?
Make the convention the use of the existing International System of Units with other units humored as parochial eccentricities. If folks particularly care they can reply with a conversion to the conventional unit.
The context of other comments and posts by the same user caused me to read it as hostile passive-aggression.
Seems unnecessary. The general convention should be that people are entitled to employ the conventions and terminology in use where they live, or that they themselves are most familiar with. I wouldn't think of demanding that someone in another country talk about their purchasing habits in terms of US dollars, for example.
She didn't. Matt said, in reply to lucidfox, "you probably just round to the nearest 1/16ths of an inch". Since she, in fact, would not round to such an absurd metric she pointed out what she would actually use. It is rather rude to declare or imply lucidfox is exceeding the bounds of what her status permits to correct a false claim about herself.
You would have a point if lucidfox had not written this post (in which a poster's use of "miles per hour" is cited as one of the offenses), but in that case I wouldn't have written the grandparent either.
Context.
Where did I demand anything?