4 ms·

The experiment is great hands on math but I would have enjoyed a discussion of variance versus expected value and the difference between short and long term ave

The experiment is great hands on math but I would have enjoyed a discussion of variance versus expected value and the difference between short and long term averages... it’s too easy to infer that everything is great because he was lucky enough to get within the target range but the likelihood of that occurring is not actually that high and was only implied by the shape of the Monte Carlo distribution in his previous post. When such experimental results are this conveniently “accurate”, amateurs in the audience may take away the kinds of wrong inferences which create “it’s a hot day so must be global warming” type of logical inaccuracies.

possiblywrong 7y ago
Author of the article here; this is a great point. This experiment initially stemmed from a nice analytical solution to the problem of computing the expected value (via generating functions as described in the post). Computing other moments, let alone the entire distribution, required some Monte Carlo simulation, as shown at the end of the first article (https://possiblywrong.wordpress.com/2019/01/09/identical-packs-of-skittles/ https://possiblywrong.wordpress.com/2019/01/09/identical-pac...) before I started the experiment. And even this histogram assumes a distribution of total number of Skittles per pack (that varies) that I had to guess at beforehand. In hindsight, the final sample distribution suggests that I probably initially overestimated the true variance, and thus also overestimated the expected number of packs I would need to inspect. In other words, this experiment arguably took longer than "average." So you're right-- this experiment could have extended into 700 packs, 800 packs... and still have been consistent with the assumed model, but I would have simply been in an unfortunate 90-th percentile possible universe where it took much longer than "average."

possiblywrong 7y ago

Author of the article here; this is a great point. This experiment initially stemmed from a nice analytical solution to the problem of computing the expected value (via generating functions as described in the post). Computing other moments, let alone the entire distribution, required some Monte Carlo simulation, as shown at the end of the first article (https://possiblywrong.wordpress.com/2019/01/09/identical-packs-of-skittles/ https://possiblywrong.wordpress.com/2019/01/09/identical-pac...) before I started the experiment. And even this histogram assumes a distribution of total number of Skittles per pack (that varies) that I had to guess at beforehand. In hindsight, the final sample distribution suggests that I probably initially overestimated the true variance, and thus also overestimated the expected number of packs I would need to inspect. In other words, this experiment arguably took longer than "average." So you're right-- this experiment could have extended into 700 packs, 800 packs... and still have been consistent with the assumed model, but I would have simply been in an unfortunate 90-th percentile possible universe where it took much longer than "average."