Re: a simple(?) probability question...



On Jan 29, 10:34 pm, "Randy Poe" <poespam-t...@xxxxxxxxx> wrote:
On Jan 29, 8:23 pm, "Joe" <jconcor...@xxxxxxxxxxx> wrote:

On Jan 29, 3:04 pm, "Randy Poe" <poespam-t...@xxxxxxxxx> wrote:
What I mean by the 50:50 chance for any year is this. For any single
year in the 100
year time span the storm will occur or will not occur in that year.That's correct.

There are only two possible
outcomes in any one given year and they are equally likely.That's incorrect. If the probability of a storm is 0.01, then the
two possibilities are:
1. Storm occurs, probability 1%
2. Storm doesn't occure, probability 99%.

Would you agree that means 50:50 chance.No, I would not agree that "two possibilities" implies "equally
likely".

It is not equally likely that you will be killed tomorrow by a
meteorite,
or that you won't. One of those possibilities is much more likely than
the other.

It does not mean there will be 50 storms in a 100 year span. The
expected outcome for the
100 year span is one storm.A 50% chance of a storm in each year means that in 100 years
there will be on average, 50 storms.

Also, there is no reason to expect that
the storm is more likely to occur in
year 75 than in year 10. The Poisson function gives prediction of a
30 or so % chance for a storm within
the first 50 years of a 100 year term. That doesn't make sense to me.
That would say you have a 70 or so %
chance for it in the last half of the century. What natural causes
would make that so?I agree that doesn't make sense. I think you're misinterpreting
something.

The Poisson distribution is f(k,lambda) = exp(-lambda)*lambda^k/k!
for the probability of k occurences, where lambda is the expected
number of occurrences in the time interval.

For a 100-year period, lambda = 1. For a 50-year period, lambda=0.5.

So that means f(1, 0.5) = exp(-0.5)*(0.5) = 0.3

Ah. Yes, that means that the probability that exactly 1 storm
occurs in the first 50 year period is 0.3, without saying
what happens in the next 50 years. You are making the
mistake that the only other possibility, if exactly 1 storm
doesn't occur in years 1-50, is that exactly 1 storm occurs
in years 51-100. That's not true. Included in all those 30%
of cases where exactly 1 storm occurs in the first 50 years
are cases where no storms occur in the next 50, 1 storm
occurs in the next 50, or more than 1 storm occurs in the
next 50.

I think the extrapolation to 10000 years changes the whole process and
requires a completely different
model.Your intuition on this point, as on so many points in this discussion,
is incorrect. I don't mean to be so blunt but you really aren't
correct on the things you're insisting on.

- Randy
Thanks for your clear explanation and forthright statement. I retract
all my previous comments
on this and accept the accuracy of your presentation on it. Thanks
also for your patience in this
dialogue.
Joe

.

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