Class 26 – Tuesday December 14, 2010

Last class.

Started out writing the final exam. It should have questions about

  1. Fermi problems. Estimation. Do the numbers make sense?
  2. Interest computations, credit card and mortgage debt. Problems that can be worked with known tools rather than problems that depend on formulas.
  3. Unit calculations. Conversions, manipulations, metric prefixes. Write the words, use the Google calculator.
  4. Averages. Mean (weighted), median, mode.
  5. Linear functions and models, slope, intercept. Regression (trendlines).
  6. Excel. Charts, histograms, what-if?
  7. Percentages. The 1+ trick. Increase and decrease. Inflation.
  8. Probability. (Not much since I taught that late and hurriedly.)

In the remaining time I introduced Poisson processes. I started with the fill-in-a-grid-with-heads-and-tails exercise. About 1/8 of the sequences of four tosses should be HHHH or TTTT so for 64 tosses there should be about 61/8 runs of four. The actual statistic from the class experiment was just 2.2, showing that people tend to think after three in a row that it’s time for the sequence to correct itself. When we read the same data vertically the average number of runs was about 4. Much bigger, though still not nearly the expected 7.

Runs do happen. If a million people flip a coin 20 times then (on the average) one of them will see 20 heads and one will see 20 tails. Those people will be surprised, but we won’t.

I described waiting for a gap in traffic as a Poisson process.

Then we talked about events that were more likely to happen if you hadn’t seen one in a while: trains at the T stop, the return of a fashion statement. Things more likely not to happen if you haven’t seen one lately? Perhaps seeing whales on a whale watch.

A good class to end with. I may blog one more time after the final exam next week. I expect to resume in the spring.

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