Re: probability definition

2001-03-03 Thread Richard A. Beldin

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I'm glad to hear that somebody has his eye on the ball. Unfortunately, a
designation of a region like "western Puerto Rico" means so many
different things to so many different people, that I disbelieve its
utility. With the definition you quote, we should have a 100% chance of
precipitation almost every day.

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Re: basic stats question

2001-03-02 Thread Richard A. Beldin

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The suits and ranks of cards in a bridge deck certainly can be presented
as independent sample spaces which we use as components of a cartesian
product. Whether one does so or not is a matter of choice. I am on
record as favoring the presentation as the cartesian product. Even the
sample mean and variance can be seen this way, in fact, every vector
valued random variable can be cast in the form of a random vector from a
cartesian product.

My point is that if we introduce independence as an attribute of sample
spaces which we proceed to study as one, we can better motivate the idea
of independent random variables and independent events.

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Re: probability definition

2001-03-02 Thread Richard A. Beldin

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The "definition" via axioms provides a mathematical structure that we
interpret either as "relative frequency" or as "degrees of belief".
Indeed, I think that any phenomenon which satisfies the axioms can serve
as an "interpretation". As they say, "If it walks like a duck, ...".

As far as the probability of rain tomorrow, I always explained to my
students that the language is so imprecise that the numerical value has
only rhetorical utility. We need to know:
1) How much rain in cm. ?
2) In which locations?
3) During what time span?

Does 70% probability mean that it rains in 70% of the locations or 70%
of the time or what?

Your instincts are correct. That example is severely flawed because we
have not made the experiment clear.

Continue to question the simple examples. You will learn from it.

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Re: Bg/Time data extrapolation?

2001-02-22 Thread Richard A. Beldin

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Given the assumption that blood glucose levels have a circadian rhythm,
you might think of a closed orbit as a model. If you had more than one
24-hour period of data, you could get started. It talkes all of your
2-hour interval observations to get the equivalent of ONE observation on
the orbit. To understand the impact of food intake and other variables,
a very extensive study would be required. On the other hand, I would
hazard a guess that someone has already done this. Try
http://www.Search4science.com/ for a search with terms like glucose
level  and circadian rhythm. Good luck.

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