Re: Modeling freight car distribution.

Tim O'Connor

Oops. My calculation was wrong. If you have ONE box car on
your layout at a time, and .14% of the fleet is Monon, then
the expectation is 40% that at least ONE of those days during
the year, the car will be a Monon car.

But if you have 100 box cars on your layout, then the expectation
on any given day is 13%, while the probability that no Monon box car
will show up within a year is .00000000000000000000619%. In other
words, there's a snowball's chance in Hell that no Monon box car
will show up.

If you have a layout with 500 box cars, then the daily chance of
at least one Monon box car showing up increases to 50%. And the
chance that at least one will show up within a week's time is
more than 99%.

Just because freight cars are proportionally few, doesn't mean
they are necessarily unusual visitors. I think that one should
do this simple calculation based on the number of cars of that
type on your layout, starting with your "average" of say, 25
cars from "eastern" railroads. Then you may find you really have
90 or 100 models that have a high likelihood of showing up every
5 or 10 operating sessions. You can calculate probabilities for
each and then proportion the number of slots (e.g. 25 x 10 days)
to get a nice, variable but realistic mix of freight cars. Or
you could just program the probabilities into your computerized
switchlist program, and have it produce a theoretically realistic
mix every day...

And therefore, the probability that NONE of the Monon box cars
showed up in a year's time in any particular location is less
than 6%... Or put another way, there's a 94% probability that at
least one of the Monon box cars would show up within a year, assuming
that all box cars are equally probable. (Given your theory of random
box car assignments.)

Tim O'Connor <timboconnor@...> -->> NOTE EMAIL CHANGE <<--
Sterling, Massachusetts

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