

Probability Theory — A Primer - nickmain
http://jeremykun.com/2013/01/04/probability-theory-a-primer/

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rgarcia
If this kind of stuff interests you, you should check out the lecture videos
from Harvard's Stat 110: <http://stat110.net>. Prof. Blitzstein is hilariously
nerdy but still has a very clear presentation style (he had kind of a cult
following back when I took the course [1]). If video isn't your thing, the
article here is basically the first few chapters of the textbook [2].

[1] <http://www.youtube.com/watch?v=iAwS7vzvLnY>
<http://www.youtube.com/watch?v=TQvVLhWOiis>

[2] [http://www.amazon.com/First-Course-Probability-7th-
Edition/d...](http://www.amazon.com/First-Course-Probability-7th-
Edition/dp/0131856626)

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loup-vaillant
For a moment I thought I would read something like Jaynes book, only simpler.
Much examples and definitions, but not many ties to real world problems. It
sounds quite arbitrary, in fact.

I think that a good primer needs to talk of probabilities as degrees of belief
from the start. Then sketch the basic premises (Probabilities are encoded in
real numbers, they abide common sense, and are consistent). Then go on to the
[0, 1] interval and state the product and sum rules. We can gloss over Cox
theorem, though we probably should stress that the sum and product rules are
not axioms, but theorems based on the basic premises above.

And _then_ , one can talk about probability distributions, random variable and
"probability space", in terms of the above.

From then, one would understand why a toss of a die yields a uniform
distribution: not because the dice itself is "fair", but because we just have
no idea whatsoever which side will come up, and don't have any reason to
favour any hypothesis over the others. This distribution is not a property of
the die, but a measure of our own ignorance.

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StevenXC
I just spent some time going though this blog - very interesting stuff,
ranging from probability to code to topology to poker puzzles. Nice link.

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tom_m
If you guys like probability and real world examples, you may wish to follow
my research (and educational process) here:
<http://www.shift8creative.com/posts/social%20media>

I'll be updating it with more geeky math and how it relates to social media in
the future.

I'm not a statistician or mathematician, so I really appreciate this article
and the links in the comments. Thanks!

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polskibus
Does anyone know of a similar resource but with real world examples and
perhaps R snippets? Would be great if I could practice two things at the same
time.

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textminer
R's not going to teach you about pre-measures, Carathéodory's theorem, or
Radon-Nikodym. Break out the whiteboards!

(Then bust out R again when you want to play with stochastic processes and
Brownian motion.)

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dexter313
Quality stuff right here.

