Folks in Europe might see up to 200 per hour, due to a "new"
filament.
2) Here's an interesting application of statistics. Students
sometimes have a hard time thinking of a probability distribution
as a real, first-class object that you can do computations with.
They think outcomes are real and probabilities are somehow less
than real. So let's do an example: electoral-college votes are
relatively concrete things, while a distribution over votes is
somewhat more abstract, but there is a big advantage if you
have enough sophistication to think in terms of distributions,
so that you can add distributions rather than just adding
votes.
Specifically: On August 1st heard a TV pundit say ``If
the election were held today Kerry would probably get 289
electoral votes and Bush would probably get 232 electoral
votes'' ... which struck me as an astoundingly silly
statement. He was quick to point out that the numbers
are hypothetical, because the election was not being
held that day, but that's not the main problem. The main
problem is twofold:
* First of all, the probability that anybody will get
exactly 289 votes is very small, about two percent.
* More importantly, the winner is not required to
get exactly 289 electoral votes or any other exact number.
The requirement is to get 270 or more.
To look at the issue another way: we need to know how
solid are the tallies predicted by the polls. It is
sufficient to have a one-vote lead if it is absolutely
solid, but far from sufficient to have a large lead in
the polls if the polls have an even larger uncertainty.
This is easy to understand if we think in terms of
probabilities, rather than thinking in terms of votes.
To make a long story short, the probable outcomes (based
on polling data, as of August 3rd) are as follows:
. Kerry Win Bush Win Tie
. 93% 6% 1%
To judge the size of the ``convention bounce'', compare
this with the numbers from a few days earlier: Kerry 84%,
Bush 15%, tie 1%.
I hope we can have a discussion of the statistical
principles without getting into a partisan wrangle about
the applications and implications for a particular race.
Don't shoot the messenger. I didn't select or fiddle the
data.
Note that the candidates already know this stuff. These
guys are consummate poker-players. The know the odds,
even if they don't necessarily feel like explaining the
odds to other players and/or bystanders.
Now if we could just impart to certain common-taters a
modicum of intelligence and a modicum of respect for
the audience's intelligence....