John
This is pretty sweet. I'd like to distribut it tomy students via Google
drive, with your permission, I'm moving away from using a web site as ours
is cumbersome and not user friendly.
So.. If you don't mind, I'd appreciate an ok to pass on to my admins.
Don McQuarrie
Chem/geology
UW in the High School
KE7ZDA
Lynden HS
Lynden, WA
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Sunday, November 04, 2012 12:24 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] introduction to probability
On many occasions over the years people (on this forum and elsewhere) have
asked where to find an introduction to probability. I've never found a
really good answer. There are a couple of good chapters in Apostol volume
II, but that's not super-widely available, and it might be over the heads of
some students.
A lot of the other stuff that's out there is IMHO unclear, unsophisticated,
and/or not entirely correct.
At the moment, the table of contents is:
1 Intuitive Representations
1.1 Disk Representation
1.2 Histogram Representation
2 Many Different Probabilities
3 Probability Measure
3.1 Definition
3.2 Some Examples
3.3 Abstract Distributions versus Numerical Distributions
3.4 The Definition of Average
4 Chains of Independent Events
5 Combinations
6 Random Walks
6.1 Unbiased
6.2 Biased
7 Sampling
7.1 Basic Random Sampling
7.2 Some Statistics Jargon
7.3 The Meaning of Error Bars
7.4 Points versus Distributions
8 Convergence of Distributions
8.1 Convergence of Moments
8.2 Distributions: The Right Way
8.3 Distributions: The Wrong Way
8.4 Convergence of Cumulative Distributions
8.5 Reconstructing the Distribution : Technical Details
9 References
Perhaps the most salient feature is the use of the axiomatic set-theory
definition of probability (as opposed to the frequentist approach). I find
this to be simultaneously simpler, more intuitive, more sophisticated, and
more useful.
Some of you may have seen earlier fragments and/or drafts of this thing.
Stuff that is new in the last few days includes:
The totem-pole picture is a way of seeing how 35 little distributions add up
to make a big distribution. It took me a while to think of this
representation, but I'm pleased with the result:
Note that your typical spreadsheet program provides a STDEV() function that
contains a fudge factor of sqrt(N/(N-1)). Where's That From? It's
virtually never what you want. It's certainly not an unbiased estimator in
the sense of using the sample standard deviation to estimate the population
standard deviation. You'd often be better off with a fudge factor of
sqrt(N/(N-1.5)) but even that isn't perfect ... and sometimes you want no
fudge factor at all.
Hint: STDEVP() instead of STDEV(). http://www.av8n.com/physics/probability-intro.htm#sec-converge-moments
Also, it is quite possible to talk about pointwise convergence of
distributions, even there is a continuous (not discrete) distribution of
zero-width points.
The trick is to look at the /cumulative/ probability distribution. http://www.av8n.com/physics/probability-intro.htm#sec-converge-cume