Only ten students in class today – but it was a lively one. I did the runs experiment – students fill in an 8×8 grid with imagined random heads and tails, writing left to write row by row. Counting runs of four (HHHH or TTTT, with HHHHH counting as two runs of four) by rows we found an average of 1.3 among the 61 possible places they could occur. Counting column by column the average was 2.3. Not a very successful result – there should have been nearer to 61/8 = 7+ on average. That said, there’s a meta-sampling error problem. I do this experiment often, so some of the time I will get unsatisfactory results. I should even be able to predict how often that will happen.
But the underlying point of the exercise was OK. There were more runs counting up and down than across. People easily admitted that after several heads they consciously evened things out with a tail.
I talked about crossing the street – waiting for a gap when the cars passing come from a Poisson process. One student said he actually thought about that when wondering about Storrow drive. I put up the Nerd Sniping cartoon at https://xkcd.com/356/ – I’m not sure they found it as funny as I do (I’m a nerd.).
One student asked whether tossing three coins was the same as tossing one coin three times. She was apologetic but I cheered. It’s the best way to explain that coins
After class I looked at the times and found this: How Not to Be Misled by the Jobs Report, where the author says at one point “Human beings, unfortunately, are bad at perceiving randomness.”
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